Basically, the concept is that people kill/injure themselves to the point where reproduction is no longer possible whilst doing something surrealistically stupid. By insuring that their stupid genes to not spread, they ultimately help humanity and thus recieve an award.
While the concept is funny enough, the actual awards are usually very mean spirited.
Smartass: What, nominate you two for the Darwin award?
Dumbass: No, I was wondering if you wanted to play while he's in the hospital.