In Israel, we read תזריע-מצורע this Shabbat. The Torah tells us that if a woman gives birth to a male, he must be circumcised on the eighth day. Many points are learned from this Pasuk.
The mentioning of the eighth day, teaches that one may violate Shabbat if the eighth day falls on Shabbat.
Another point is that the act of Brit Milah fulfills a positive commandment for which we make a Bracha, על המילה. Circumcision and קרבן פסח are the only two positive commandments where there is a punishment for non fulfillment. (The punishment for both is Karet.)
The third aspect of ברית מילה is that it makes the child a בן ברית, an official Jew. He is now qualified to offer a קרבן as a Jew. This is why there is a second Bracha at a Brit, להכניסו בבריתו של אברהם אבינו. Shabbat Shalom