Uvayom ha-Shemini yimol b’sar orlaso ... on the eighth day, the flesh of his foreskin shall be circumcised (Shemos 12:3). The Talmud [Shabbos 132a] derives from the seemingly redundant use of the word day [the verse could have said simply on the eighth] that the mitzvah of circumcision overrides the prohibition of inflicting a wound on Shabbos.
The Talmud elsewhere declares that a mumar l’chalel Shabbos - one who willfully desecrates the Shabbos - is considered to be a mumar l’kol ha-Torah kulo - one who would willfully desecrate the entire Torah. Observance of Shabbos has always been the standard against which a Jew was judged regarding his conformity to halachic requirements. The stringencies regarding Shabbos observance are well known; the Talmud only permits violating Shabbos law for a person suffering from a life-threatening illness or situation [pikuach nefesh] because it logically concludes that it is preferable to allow him [the person threatened] to desecrate one Shabbos so that he might fulfill many Shabbosos. Whereas the general leniency that prevails in a pikuach nefesh situation is based on a derivation from a pasuk [vechai bahem v’lo sheyamus bahem - he shall live by them (mitzvos) and not perish because of them] - the Talmud did not seem to find this to be sufficient cause to put aside the laws of Shabbos. Thus, it is somewhat difficult to understand why the mitzvah of milah - overrides Shabbos. Why not postpone circumcision until Sunday when the eighth day falls on Shabbos?
We might be tempted to suggest that the importance of milah is the fact that it is this act that most clearly identifies a person as being part of the Jewish nation. Indeed, circumcision is one of only two mitzvos aseh - positive mitzvos - punishable by kares! We find that an orel - a non-circumcised Jew - is not permitted to partake of the korban Pesach - the sacrifice most clearly connected to Jewish peoplehood. We might suggest that just as the Talmud rules that a non-Jew is subject to capital punishment for observing Shabbos, so too the orel must be circumcised - even on Shabbos - so as not to be culpable of non-sanctioned Shabbos observance.
In truth, however, this is not really a valid solution to our question, for the halachah teaches that if there is a medical reason [e.g., jaundice] to refrain from circumcising on the eighth day, milah does not override Shabbos. For example, if the eighth day fell on a Friday and medical considerations precluded circumcising the child on that day, we would wait until Sunday to perform the ceremony since milah she’lo bizmano eino docheh Shabbos - milah performed not at the specified time does not override Shabbos. Similarly, if there is a question as to whether the baby was born on Friday or Shabbos [e.g., if the birth took place bein hashmashos - between sunset and the beginning of night - on Friday], the circumcision would be delayed until Sunday. It could not be done on Friday, for it is possible that the baby is only seven days old. It cannot be performed on Shabbos, because if we consider the baby to have been born on Friday, he is nine days old on Shabbos and milah performed not at the specified time does not override Shabbos.
Both Shabbos and milah are referred to as os - a sign - signifying the special relationship between G-d and the Jewish people. We also find that tefillin are referred to as an os. Interestingly, the os of tefillin does not override Shabbos, i.e., we do not lay tefillin on Shabbos since we already have an os [of Shabbos]. Why not say the same thing as regards milah; i.e., since Shabbos is already an os there is no reason why the os of circumcision should override it.
I would like to suggest that the os of milah is composed of two distinct components. On the one hand, milah represents a physical sign that we make in our bodies to demonstrate that we consider ourselves to be part of the covenant of Avraham, with all of the attendant restrictions and benefits. That part of the os of milah would not override Shabbos, just as the os of tefillin is set aside for Shabbos. Our observance of Shabbos itself is the ultimate evidence of our acceptance of our unique relationship with G-d and, indeed, a non-Jew who observes Shabbos is liable to the death penalty because he is assuming a covenantal relationship that does not exist.
At the same time, milah has a second os component. The Talmud [Shabbos 135a] explains that milah is done on the eighth day as an indication of the woman’s returning to a state of ritual purity after childbirth. The Torah rules that when a woman gives birth to a boy, she is tamei for seven days and milah is done on the eighth. But if a woman gave birth through Caesarian section, the child’s milah would not be performed on Shabbos, since she never became tamei. Similarly, if the milah is done after the eighth, it does not override Shabbos, since it does come to demonstrate her release from her state of ritual impurity.
While the os of Shabbos observance is greater than the os of tefillin or of the act of circumcision and is therefore not discarded, the separate os of milah that comes to signify the ascension from tumah to taharah does not find expression in Shabbos and it is for this reason that only milah on the eighth day, when we actually celebrate the mother’s ascension, overrides Shabbos.