As a man of God, Timothy was told to follow after, or pursue, godliness.  The Greek word used for godliness in this verse is eusebeia. Eusebeia is a real, true, vital spiritual relationship with God and is the opposite of threskeia (religion) which relates to the acts of religious observances or ceremonies.  Religion is an outward act performed by sense knowledge man in an attempt to show God or others his piety. Godliness is a true spiritual relationship which comes from having holy spirit within and walking with God.

   The book of Timothy was written to a young leader in the body of believers to whom Paul was passing on much of the responsibility of keeping the Word alive and moving. Eusebeia is used eight times in the book of 1 Timothy.

1 Timothy 2:1-4
   I exhort therefore, that, first of all, supplications, prayers, intercessions, and giving of thanks, be made for all men;
   For kings, and for all that are in authority; that we may lead a quiet and peaceable life in all godliness and honesty.
   For this is good and acceptable in the sight of God our Saviour;
   Who will have all men to be saved, and to come unto the knowledge of the truth.

   We want to live honest, quiet, peaceable lives walking in all of the true, vital, spiritual relationship with God that is available. Therefore, God exhorts that we talk with Him, we make requests of Him, we ask Him to intercede, and we give Him thanks when it comes to living in this world where men are ruled by their own selfish needs and desires and where men have authority over us via governments.  It is by exercising our true, vital, spiritual relationship with God in prayer for those who have influence around us in the world that we are able to live a quiet and peaceable life in all godliness and honesty.  We want to walk in the abundant spiritual relationship that God has made available without interference from the laws and rules of men.  That does not mean we do not live within the confines of the laws of our lands.  It means looking to God to keep our lands free from laws and decisions of men that would obstruct our freedom to live according to God and His Word.  It means praying for kings and those in authority.  It means going to God and trusting Him when it comes to living in this world.  The focus is not on the act of prayer to show men how religious we are;  the focus is on the true, vital, spiritual relationship we have with God that allows Him to work in the situations in our life that are influenced by the men around us.
   It is God's will that ALL men get born again, saved, and ALSO that all men come unto THE knowledge of THE truth.  To that end we pray for men to believe and we walk with God in that true, vital, spiritual relationship.  For this is good and acceptable in the sight of God who sent His son to save us and to make it available for us to live our lives in godliness.

1 Timothy 3:16
   And without controversy great is the mystery of godliness: God [WHICH - the Greek word "ho" - means: Which] was manifest in the flesh, justified in the Spirit, seen of angels, preached unto the Gentiles, believed on in the world, received up into glory.

   "The mystery of godliness" is the Greek genitive of origin and can be understood in English as "The Great Mystery which produces godliness."   The Great Mystery is that which God hid in Himself regarding the spiritual relationship that would be available to us in this day and administration of grace.  We are able to walk in a true, vital, spiritual relationship with God today because of the fullness of that which God made available to us on the day of Pentecost.  The richness of that which we received was so big that God hid the knowledge of it in Himself until He revealed it to the Apostle Paul.  It is the knowledge of that which we received that produces a true, vital, spiritual relationship with God.  Here in Timothy, the Great Mystery is outlined in this verse:

It was manifest in the flesh: On the day of Pentecost it became available for all - Jews and Gentiles - to get born again and have holy spirit within.  It became available to walk in a true, vital, spiritual relationship with God.  The Mystery of what God prepared for us before the foundations of the world was manifest in the flesh and seen for the first time as the 12 Apostles spoke in tongues on that wonderful day.  A knowledge of that which came on the day of Pentecost and how to operate all nine manifestations of the spirit in our life produces godliness in our walk.

It was justified in the Spirit: In the new birth all - Jews and Gentiles - are spiritually justified.  Because of the walk of Jesus Christ and our acceptance of his substitution for us we have received from God justification.  Spiritually it is "just as if we never sinned."  The Great Mystery includes our justification.  A true, vital, spiritual relationship includes walking with God in the knowledge of our standing before God without any sense of sin, guilt, or condemnation.  The knowledge of our justification produces godliness in our walk.

It was seen of angels:  Ephesians 3:9-10 says And to make all men see what is the fellowship [administration] of the mystery, which from the beginning of the world hath been hid in God, who created all things by Jesus Christ [not in text]: To the intent that now unto the principalities and powers in heavenly places might be known by the church the manifold wisdom of God,  A knowledge of the Great Mystery of our administration is made known to all, including angels and spiritual powers, by us: by the church.  A true, vital, spiritual relationship with God includes making known the administration of the mystery to all principalities and powers in heavenly places.  It means walking a spiritual walk in which we recognize the existence of spiritual powers in the world and the true spiritual nature of life.  As we make known the mystery of that which God has given to us, the knowledge of this mystery produces godliness in our walk.

It was preached unto the Gentiles (nations): Ephesians 3:8 says Unto me [Paul] who am less than the least of all saints, is this grace given, that I should preach among the Gentiles the unsearchable riches of Christ;  Unsearchable is untrackable.  The knowledge of what was to become available and that all nations - Jews and Gentiles - were to be included was not trackable in the Word of God given in the Old Testament.  This mystery was first made known to the Apostle Paul after the day of Pentecost.  The grace of God given to us is available to every man!  A true, vital, spiritual relationship with God includes teaching the world about that which God has made known unto us.  As we make it known, by preaching, the knowledge of this mystery produces godliness in our walk.

It was believed on in the world: Romans 10:9-12 says That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved. For with the heart man believeth unto righteousness; and with the mouth confession is made unto salvation.  For the scripture saith, Whosoever believeth on him shall not be ashamed.  For there is no difference between the Jew and the Greek [Gentile]: for the same Lord over all is rich unto all that call upon him.  When we share with the nations what it takes to get born again and receive the great benefits of the mystery some will respond by believing.  Making known the mystery includes taking action - believing - that which you hear.  A true, vital, spiritual relationship with God includes believing the Word of God once we hear it.  As we act on a knowledge of the mystery of God, it produces godliness in our walk.

It will be received up into glory:  A knowledge of the Great Mystery of the grace of God includes our hope for the return of Christ and our gathering together unto him.  As we walk in a knowledge of the mystery of God we look toward our hope.  The believers will be given new spiritual bodies and meet the Lord in the air.  It could be today!  A true, vital, spiritual relationship with God includes keeping our eyes on the hope of Christ's return.  Walking in a knowledge that we will be received up into glory (as was the Lord Jesus Christ) produces godliness in our walk.

   This summary of the whole mystery was given by Paul to Timothy to produce godliness in opposition to the religious acts that all too often replace the true, vital, spiritual relationship with God in many peoples lives.

   In the context of this verse Timothy was told that some believers would depart from the true, vital, spiritual relationship of godliness and begin to teach others a variety of religious practices such as forbidding to marry and don't eat meat.  Religion is the OPPOSITE of godliness.  You cannot walk in a true, vital, spiritual relationship with God if your worship consists of ceremonies and religious acts.  The Word of God calls these acts a departure from right believing, doctrines of devils, hypocrisy, and profane old wives' fables.  We are to practice [exercise] godliness not religion.  That does not mean that we don't sometimes have a ceremony or stop eating meat for awhile.  It does mean that the things we do will be a reflection of what is right to do at a particular time because our true, vital, spiritual relationship with God is directing our paths.  When the acts become more important than our relationship with God then we are just being religious.  What we do outwardly should be a manifestation of our inward walk with God.  We do not practice religious acts to reach or please God.  We have a relationship with Him and we act because we already have access to Him and we already are pleasing to Him.

   Wholesome words - the words of the Lord Jesus Christ - doctrine - is to be according to the standard of our real, true, vital, spiritual relationship with God and not according to the commandments and doctrines of men.  Doctrine is how to believe rightly!  What we teach regarding how to believe rightly is to always be according to the standard of godliness.  The man who teaches otherwise follows this downward path:

1 Timothy 6:4-5
   He is proud, knowing nothing, but doting [having a sick appetite] about questions and strifes of words, whereof cometh envy, strife, railings, evil surmisings,
   Perverse disputings of men of corrupt minds, and destitute of the truth, supposing that gain is godliness: from such withdraw thyself.

   It begins with pride.  A man thinks he knows it all and has himself as the standard for truth rather than God and His Word.  The Word of God says this man KNOWS NOTHING!  Then he begins getting a sick appetite for questions.  He becomes hungry to question the Word of God and find fault with it.  He begins fighting over words.  These actions produce envy, strife, railings, evil surmisings, and perverse disputings.  This man's mind has become corrupt and is destitute [without] a knowledge of the truth.  In the end this man comes to the conclusion that gain [material abundance] is godliness.  He thinks that a true, vital, spiritual relationship with God is the same thing as having THINGS in abundance.  The Word of God says that when a man acts like this we are to withdraw or excuse ourselves.

1 Timothy 6:6
    But godliness with contentment is great gain.

   In contrast to the man who thinks that gain is what godliness is all about, a real, true, vital spiritual relationship with God and being content with what God provides you is very great gain.  No matter what it is that you have or want in this life you can be content if your focus is on your relationship with God.  In Philippians 4:11 Paul said that he had learned to be content in whatever situation he found himself.  He could live in abundance and he could live in need.  The key to contentment in your life is godliness.  If your relationship with God is such that He is the supplier of all your need then you can be content with that which you have.  Godliness with contentment is very great gain.

   In conclusion, pursue a real, true, vital, spiritual relationship with God.  All other things will fall in place when your walk with God is right.