Clap, or The Clap is a slang term for gonorrhea. It is not a new bit of slang by any means, having been in use since at least 1587, when it appeared in the Mirror for Magistrates, a collection of English poems from the Tudor period.
"But they doe thinke such sweetenes in renowne,
They deeme on earth is all the greatest hap;
They nothing feare the hurt of falling downe,
Or little rome in Lady Fortune's lap.
They give no heed before they get the clap.
And then to late they wish they had bin wise,
When from the fall they would, and cannot, rise."
--Mirror for Magistrates, How King Malin was slayne by his brother King, 3
We aren't certain, but our best guess is that this comes from the Middle English claper, which in turn probably comes from the Old French clapoire, which literally meant a rabbit burrow, but was used as slang to refer to a brothel. This in turn came to refer to STDs, particularly nasty ones that could give you nasty oozing buboes. This was eventually pared down to just gonorrhea.
This is one of the oldest slang terms in common usage, although the cruder monosyllables are older still. Damn also has it beat by about a century. Amazingly, none of these have yet managed to jump the barrier between informal, vulgar speech and formal usage in over 400 years of popular usage. Clap has come close to jumping the respectability barrier, appearing in health classes and educational materials across the US, and appearing in most dictionaries, but it is still considered informal or colloquial by most sources.