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 the 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 (eg, in Judiasm and Islam) or cultural reasons (eg, to allegedly reduce lustful thoughts as in Victorian era Anglo-Sason countries -- some of which continues, chiefly in North America), or health reasons. It is now almost non-exitent in most of the devleoped world, with the notable (though decreasing slowly) case of the United States.
Health benefits are increasingly denied, and most medical societies around the world now recommend against routine use. Formerly, after a small study of cervical cancer rates in Jewish women, circumcision was claimed to lower the risk for cancer of the cervix in sexual partners. And perhaps to reduce the chance of cancer of the penis. The speculation was that smegma (accumulated secretions between glans and foreskin) was the cause. These studies have lost credibility if only because of neglected variations in cleaning habits, and that further studies have failed to confirm the effect. It also claimed, with still less grounds, to decreases the risk of urinary tract infections. A large and credible study of HIV trnasmission has given very good grounds for decreased risk of male HIV infection in circumcized males. As the skin of the glans in uncircumcised males is the thinnest of any human skin, the possible reason for this may be that such thin skin is easier for the HIV virus to pass through. As there is much not understood about viral transmission generally, this is, as with all statistically based conclusions, not a satisfactory guide for individual decisions. Whether on behalf of one;s self, one's adult sexual partner, nor one's infant.
Circumcison is not without risk. There are complex and dense nerve networks in the foreskin and the glans which will be inevitably damaged to some extent during any circumcision. And in the case of infants, whose tissue development is not complete, there is some quextion as to where the boundary between the galns and foreskin is. Separation of the tissues does not occur, in the normal case, until some time after birth. It can even be delayed until puberty. Infant circumcision nearly always involves a forcible separation along the presumed line of (would have been) separation, sometimes frankly surgical. There is considerable pain, and since anethesia has not been traditonal or common; infants consistently protest. Problems with even professional medical circumcision have included infection, gangreen, and forced amputation of part of all of the penis. The formerly alleged health reaaons for included inability to retract the foreskin (almost never a problem in practice when left alone, even when delayed) and inability to return the foreskin around the glans after retraction. Neither is actually at all common, and so the balance of risks is not obvious.
In a BSDM context, male circumcision has the usual effect of reducing cock sensitivity, thus alllowing more extended stimulation. This may not always be desirable as there is some suspicion that older men become impotent sooner than otherwise because of just this reduction in stimulation.
In females, circumcision is the partial or complete removal of the prepuce (clitoral hood), labia minora or even clitoris. there are similar consequences for reduction in stimulation as in males, but as female arousal is more varied, and less concentrated, than is male arousal, the consequences are less predictable.