{c} This is my covenant, which ye shall keep, between me and you and thy seed after thee; Every man child among you shall be circumcised.

(c) Circumcision is called the covenant, because it signifies the covenant and has the promise of grace joined to it: a phrase that is common to all ordinances.

Wesley's Notes

17:10 The token of the covenant, is circumcision, for the sake of which the covenant is itself called the covenant of circumcision, Acts 7:8. It is here said to be the covenant which Abraham and his seed must keep, as a copy or counterpart, it is called a sign and seal, Rom 4:11, for it was. A confirmation to Abraham and his seed of those promises which were God's part of the covenant, assuring them that, in due time, Canaan should be theirs: and the continuance of this ordinance, after Canaan was theirs, intimates, that that promise looked farther, to another Canaan. An obligation upon Abraham and his seed to that duty which was their part of the covenant, not only to the duty of accepting the covenants and putting away the corruption of the flesh, which were primarily signified by circumcision, but in general to the observation of all God's commands. They who will have God to be to them a God, must consent to be to him a people. Now,
1. Circumcision was a bloody ordinance, for all things by the law were purged with blood, Heb 9:22. See Exo 24:8. But the blood of Christ being shed, all bloody ordinances are now abolished. Circumcision therefore gives way to baptism.
2. It was peculiar to the males, though the women also were included in the covenant.
3. Christ having not yet offered himself for us, God would have man to enter into covenant, by the offering of some part of his own body, and no part could be better spared.
4. The ordinance was to be administered to children when they were eight days old, that they might gather some strength to be able to undergo the pain of it.
5. The children of the strangers were to be circumcised, which looked favourable upon the Gentiles, who should, in due time be brought into the family of Abraham, by faith. Here is,
(1.) The promise made to Abraham of a son by Sarai, that son in whom the promise made to him should be fulfilled, that he should be the father of many nations, for she also shall be a mother of nations, and kings of people shall be of her, Ge 17:16. Note, God reveals the purposes of his good - will to his people by degrees. God had told Abraham long before, that he should have a son, but never 'till now that he should have a son by Sarai. The blessing of the Lord makes fruitful, and adds no sorrow with it; no such sorrow as was in Hagar's case. I will bless her, with the blessing of fruitfulness, and then thou shalt have a son of her. Civil government and order is a great blessing to the church. It is promised not only that people, but kings of people should be of her; not a headless rout, but a well modelled, well governed society.

Jamieson-Fausset-Brown Bible Commentary

10. Every man child among you shall be circumcised-This was the sign in the Old Testament Church as baptism is in the New, and hence the covenant is called "covenant of circumcision" (Ac 7:8; Ro 4:11). The terms of the covenant were these: on the one hand Abraham and his seed were to observe the right of circumcision; and on the other, God promised, in the event of such observance, to give them Canaan for a perpetual possession, to be a God to him and his posterity, and that in him and his seed all nations should be blessed.

Matthew Henry's Concise Commentary

17:7-14 The covenant of grace is from everlasting in the counsels of it, and to everlasting in the consequences of it. The token of the covenant was circumcision. It is here said to be the covenant which Abraham and his seed must keep. Those who will have the Lord to be to them a God, must resolve to be to him a people. Not only Abraham and Isaac, and his posterity by Isaac, were to be circumcised, but also Ishmael and the bond-servants. It sealed not only the covenant of the land of Canaan to Isaac's posterity, but of heaven, through Christ, to the whole church of God. The outward sign is for the visible church; the inward seal of the Spirit is peculiar to those whom God knows to be believers, and he alone can know them. The religious observance of this institution was required, under a very severe penalty. It is dangerous to make light of Divine institutions, and to live in the neglect of them. The covenant in question was one that involved great blessings for the world in all future ages. Even the blessedness of Abraham himself, and all the rewards conferred upon him, were for Christ's sake. Abraham was justified, as we have seen, not by his own righteousness, but by faith in the promised Messiah.