Flex is a fairly new technology (not a board) that has been adopted by most board companies for select boards. It basically allows the board to bend under pressure rather than being rigid because of different "core" materials/designs. Slingshot was the first company devoted to an all flex line-up but most other major manufacturers offer a flex board in their line-up. They take rail abuse longer, allow for more style when on rails, they provide "give" or cushion on big landings (some would argue reducing shock on your knees), and there are many that argue they provide a certain recoil effect coming off the wake which generates additional pop.
There are plenty of people that hate on flex boards, but almost every new board company that has come out in recent years has predominantly a flex line-up... and every major manufacturer has seen it fit to make at least one, so to me the proof is in the pudding
Jason Hammons at the American Boat Center in Knoxville is a great resource for Slingshot and I'm sure you could demo something there... or ask Pete and the guys at WakeNation when spring comes around and I'm sure they can hook you up with a demo flex board on the cable.
Check out some of the vids here for more discussion: http://www.slingshotsports.com/wake_videos