There are a few occasions in the Torah where man is given a covenant bewteen him and G-d, and none are more physically important than the brit milah, the covenant of circumcision. This is referred to in the Torah in Genesis 17:10-11. Others say that the ritual comes from early child sacrifices.
The circumcision is performed by a mohel, a specially trained rabbi with years of training and experience. The ritual is rarely performed with women present, and is done without an anaesthetic on the eight year old boy. There is an exception to this date - if the child is unwell and thus cannot have it performed at that date. Even on Shabbat, when cutting is normally prohibited, is the ritual allowed.
Primarily, this ritual has come to identify Jews from non-Jews. Originally, just the tip of the foreskin was removed in the procedure, but later Jews learnt how to hide this with the aid of a small cap, so they would not be segragated against in the Roman sports events. In protest, the rabbis of the time decreed that the whole of the foreskin should henceforth be removed, which disabled the Jews from hiding their identity. The ritual has remained the same ever since.