The Torah specifies that the circumcision must be performed on the eighth day after birth, even if this is a Sabbath. It is not a coincidence that the eighth commandment God gave to humanity was that of circumcision. Numbers are of great consequence in Judaism and they are often used as a code or to hint at certain concepts. When a number forms an integral part of a mitzvah, it is certainly not arbitrary. What then is the meaning of the number eight?
The significance of a number can be understood by the way it is used in the Torah, especially the first time that it occurs in the Biblical text. The number 6, which appears first as the six days of Creation, symbolizes the expansion and creation of the physical world. Sabbath, which is the spiritual dimension that forms the focus of the physical world, is the seventh day. The physical world expands to the north, south, east, west, up and down. Six has no center, it has three points on one side and three on the other (*** ***). The seventh day, the Sabbath, is the spiritual center point around which the physical world revolves. It is the Godliness within the world, the point around which the six days of physical creation are arrayed (*** Sabbath ***).
Eight symbolizes going beyond the natural world, beyond the seven days of Creation, into the realm of the supernatural. Circumcision is an act which changes and improves on nature, which demonstrates the human ability to go beyond nature into the realm of the supernatural. That is the metaphysical reason why circumcision, the eighth commandment, must always be on the eighth day.
On a pragmatic note, Maimonides, who was a physician in addition to being a great Torah scholar, explained that on the eighth day, but not before, the child is strong enough to be circumcised. In fact, current medical research regarding blood coagulation suggests that the eighth day is the earliest advisable time to perform circumcision.