The clap got its nickname from the methods of treating gonorrhea on the war front. This painful way of treatment involved two soldiers holding their comrade's arms, two soldiers holding their comrade's legs, and one soldier "clapping" his hands on the comrade's penis, discharging the fluid.
"Did you hear what Steve caught from me?"
"Yeah, the clap."
"No... I had herpes. He has the clap!?"
"Yeah... hey, now you have the clap, too!"