The word "grace" used in the verses above is the Greek word "charis." Charis, grace, can be defined as unmerited, favor from God.  It is pure giving without any strings.  Grace is not something you can earn.  In fact, grace is defined in God's word as the opposite of earning a reward by work.

Romans 4:4 Now to him that worketh is the reward not reckoned of grace, but of debt.

The root word from which charis-grace is defined is the Greek word "chairo." Chairo is used in God's Word as a greeting meaning "be well" or it means "be glad" or "rejoice!"  The grace of God is a joyful thing.  It is not a burden.

All that we have received in Christ Jesus we received not by our works, but by the grace of God:

Romans 3:24 Being justified freely by his grace through the redemption that is in Christ Jesus.
Ephesians 1:7 In whom we have redemption through his blood, the forgiveness of sins, according to the riches of his grace;
Ephesians 2:5-9 Even when we were dead in sins, hath quickened[made us alive] us together with Christ, (by grace ye are saved;) And hath raised us up together, and made us sit together in heavenly places in Christ Jesus; That is the ages to come he might shew the exceeding riches of his grace in his kindness toward us through Christ Jesus.  For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: Not of works, lest any man should boast.

We are justified, redeemed, forgiven, saved, made alive, raised, seated, and have more to come by the exceeding riches of God's grace.  Not because of any works we did or will do, but a free gift of God.  That is grace.

Some other Greek words related to the grace of God are:

Charisma - spiritual gifts of God's grace.  Given freely to man by God - not earned.

Charisma, gifts of God's grace, are also not taken back by God when they are not used or are used improperly.  God's grace is unmerited and irrevocable. Romans 11:29 For the gifts and calling of God are without repentance.

Luke 1:28 And the angel came in unto her [Mary], and said, Hail [chairo], thou that art highly favored[charin], the Lord is with thee: blessed art thou among women.

Ephesians 1:6 To the praise of the glory of his grace [charis], wherein he hath made [charin] us accepted [charin] in the beloved.

Romans 8:32 He that spared not his own Son, but delivered him up for us all, how shall he not with him also freely give[charizomai] us all things?

I Corinthians 2:12 Now we have received not the spirit of the world, but the spirit which is of God; that we might know the things that are freely given[charizomai] to us of God.

Ephesians 4:32 And be ye kind one to another, tenderhearted, forgiving[charizomai] one another, even as God for Christ's sake hath forgiven [charizomai] you.

Colossians 3:16 Let the word of Christ dwell in you richly in all wisdom; teaching and admonishing one another in psalms and hymns and spiritual songs, singing with grace in your hearts to the Lord.

Colossians 4:6 Let your speech be alway with grace, seasoned with salt, that ye may know how ye ought to answer every man.

I Peter 4:10 As every man hath received the gift, even so minister the same one to another, as good stewards of the manifold grace of God.