Shabbos, Mishnah 6. This mishnah addresses the question of which remnants of the foreskin invalidate the circumcision from being considered a milah performed properly.
The mishnah lists the shreds and remnants of the foreskin that invalidate the milah. There are certain tight remnants of foreskin that constitute a problem, and as long as they are present the person has not fulfilled the mitzvah of milah, and there are others that ought to be removed but that do not prevent the person from having fulfilled the mitzvah.
Which shreds invalidate the milah:
"Basar hachofeh es rov ha'atarah" - flesh that covers the majority of the corona. The atarah is the crown at the end of the organ. If remnants of the foreskin cover the majority of it, whether along its height or along its circumference, this invalidates the milah, and the circumcision must be completed properly in order to fulfill the mitzvah.
A further practical difference: the halachah is that an arel - someone who was not circumcised at all, or who was not circumcised properly - may not eat Terumah. Therefore a person who is left with shreds that invalidate the milah does not eat Terumah, even if he is a kohen.
Ba'al basar - because of appearances:
This is a case where the child is very heavy, and the milah was in fact performed completely, but the fat covers that part of the organ and creates the appearance that invalidating shreds remain. In such a case the matter must be corrected because of how it looks, and a bit more is trimmed in the course of the milah, even though by strict law the circumcision was performed properly.
He circumcised but did not uncover:
Periah is the peeling back of the membrane beneath the foreskin and drawing it downward. "Mal velo para es hamilah - ke'ilu lo mal" - if one circumcised but did not perform periah, it is as though he did not circumcise at all: if the milah was done without periah, one must go back and perform the periah in addition to the milah.
And on Shabbos: one who performs the milah without periah has desecrated the Shabbos, since he made a wound and drew blood without having fulfilled the mitzvah of milah.
In summary: in this mishnah we learned that flesh covering the majority of the corona, whether in height or in circumference, invalidates the milah and forbids the person from eating Terumah; that with a heavy child we correct the appearance even though the milah is complete; and that one who circumcised but did not perform periah is considered as though he did not circumcise at all, and on Shabbos he is even liable for desecrating the Shabbos.