Genesis 17 picks up the narrative 13 years after the birth of Ishmael in Genesis 16. At this point Abram and Sarai have been in the Promised Land waiting for the miracle of a son and heir for 23 years. At this point God speaks to Abram, tells him that he will be called Abraham and his wife Sarah, and adds that the promised son, Isaac, is only a year away. Abraham laughs at this prospect, as Sarah will do in the next chapter.
God also gives Abraham a sign of the covenant that already exists between God and Abraham: circumcision. This initiation rite wasn't unfamiliar in the Ancient Near East, God chooses something culturally appropriate to set apart Abraham and his descendants as his particular people, the ones he has called into this relationship.
Circumcision functions for Israel in the same manner that Baptism functions for the Church, it proclaims that those involved belong to the larger group, to that they are a part of the people of God.
