Berit Milah, means the "covenant of circumcision,". It is the first Mitzva commanded to our patriarch Abraham (Bereshit 17:14) and the most important sign of Jewish identity of a Jewish male.
The Berit Mila is performed on a baby boy, usually eight days after he is born. It involves the removal of the foreskin by a Mohel, a 'circumcision surgeon', specially trained to safely perform the procedure.
The Berit Mila is called popularly by one word. In Yiddish they call it: "Bris" and in most Sephardic communities: "Mila".
If the eighth day falls on a Shabbat, the Berit Mila is still performed. According to our tradition the performance of Berit Mila in its due time, overrides Shabbat. Still, except for what is needed for the actual performance of the circumcision, the rest of the Laws of Shabbat are not suspended.
Sometimes circumcision must be delayed and in extreme cases (hemophilia), suspended. If a doctor or an experienced Mohel considers that the baby is still not physically ready for the circumcision, the Berit Mila needs to be postponed until the baby is physically fit for it.
The typical case of delayed circumcision is when the baby is premature and or less than 6 pounds (this criteria varies slightly according to different schools). Other common reason to delay the circumcision is jaundice, (yellowish skin) a temporary disease, that might affect as many as 60% of all newborn babies.
A doctor should be always consulted as to when the circumcision might be done.
READ Circumcision and the Eight day,By Daniel Eisenberg, MD