A showcase is basically a combine camp with games thrown in. They will test everyone at different tasks and then schedule some games to further evaluate the talent. Many advertise as recruiting service as well. That is, they will mail your results to different schools and help market you a bit. Many will also have coaches form colleges and even pro scouts in attendance to look at the players.
From what I am learning, you have to do research as there are alot of fly by night operations that use the promise of this to make money with no real results for the player. You will probably have to travel to attend one. To get invited, just fill out a nomination form at their websites and they will send you the information.
No offense to anyone omitted, but Perfect Game and College select are supposed to be very good. My friend's son went to Blue-Grey and that didn't do much for him. He got more interest by attending college camps. I've heard good things about Team One as well. I'm sure there are others that people more qualified than I can comment on.