In the UK, Europe and USA, circumcision normally refers to a surgical process on males. It involves the partial or complete surgical removal of the foreskin (the loose tissue covering the glans) of the penis. The style in common use in the west for nearly two thousand years (since bar Kochba) is radical circumcision, in which the entire foreskin is removed. Prior to this, the commonest style amongst Jews was partial in which only the tip of the foreskin was removed.
Circumcision may be performed for religious reasons (as in Judaism and Islam) or cultural reasons (e.g. allegedly to reduce lustful thoughts as in Victorian era Anglo-Saxon countries), or for health reasons.
Circumcision is now much rarer in most of the developed world, with the notable exception of the United States and Canada where, although even there it is decreasing slowly, most boys get their foreskins removed perinatally. (This partially explains why lots of Norh American boys experiment with Prince Alberts.) Until recently, male members of the British Royal Family were circumcised; Charles, Prince of Wales, was circumcised by a Jewish mohel (Lionel Snowman). However, Diana Princess of Wales refused to allow her children to be circumcised.
In a BDSM context, male circumcision usually has the effect of reducing glans sensitivity, as the skin thickens considerably, thus allowing more extended stimulation before ejaculation. A demand for control from a Dominant may be more readily met after circumcision.
Circumcision makes genital hygiene easier because dirt cannot get trapped under the foreskin. It greatly reduces the risk of transmitting certain diseases, especially the papilloma virus (which can cause cervical cancer) and AIDS.
The circumcision operation is not without risk: there are complex and dense nerve networks in the foreskin and the glans may be damaged to some extent during any circumcision.
The typical reduction in sensitivity may not be desirable in the longer term, as there is some suspicion that older men become impotent sooner than otherwise because of just this reduction in stimulation.
In correct medical terminology, the term "female circumcision" refers only to the operation of removing a small flap of skin surrounding the clitoris (analogous to the foreskin in males), without cutting the body of the clitoris itself. For other non-medically-justified operations on the vulva (sometimes euphemistically referred to as "female circumcision"), see female genital mutilation.