Circumcision is an extremely central milestone in the life of a Jew. Aside from the fact that it is a commandment (the first ever given to a Jew) it is also the entry of the child into the covenant of Abraham and into the covenant between God and the Jewish people.
We believe that the purpose of the human being is to in fact change and improve the natural world, both physically and spiritually. Circumcision is the symbol of the ability of the human to change the physical world. It is also an indelible sign on the organ that most symbolizes the continuity of the Jewish people from generation to generation of attachment to the Jewish people.
Circumcision is based on the Biblical commandment in Genesis 17:12 and in Leviticus 12:3 where it explicitly states "the eighth day". The rationales for this are many:
1. Seven symbolizes the natural world (7 days of creation). Eight is one beyond nature, symbolizing the ability of the human to improve himself and the natural world. The circumcision is symbolic of man's ability to change, improve and add to the natural world.
2. Eight days always includes a Sabbath, so that the child's experiences the sanctity of Sabbath and a "taste of the world to come" before the pain of circumcision.
3. According to Maimonides, the eighth day is the earliest day at which the blood will clot properly in the wound and is early enough in the child's life so that the pain and trauma will not have a detrimental impact on him.