Rave valves are exhaust valves.
History - The idea has been around for a long time but really came to be in the two stroke toy market on the 1989 skidoo mach 1 583. It made it's way into the seadoo line with the 787 motor, anyone correct me, with the 96 XP 800.
It stands for Rotax Automatic Variable Exhaust. It is a simple system working off of exhaust pressure into a bellows that expands and pulls a guillotine type slide into and out of the exhaust port based on exhaust pressure and engine rpm. It gives you a lower exhaust port at lower rpm's and a higher exhaust port at higher rpm's. The power curves of the two motors are different and the rave valve operates where the two curves "cross" giving you more torque at lower rpm's and more power at higher rpm's. The idea was how can they get a higher powered motor to produce good low end torque and the rave valve was one answer that was trouble free and simple in design. It gives you the "best of both both worlds" with low port torque and high port power, although "port" in this instance is a generic term.
It works because skidoo offered multiple "types" of the 580 motor in snowmobiles, with and without the rave. The non rave had good low end power but did not rev higher and was not as powerful as the rave type. The rave type pulled hard down low and transformed into a higher reving, higher hp motor on the top end. I never liked the non rave 580, too mellow.
It originated in moyorcycle racing, transformed to sleds and now most of the major sled manufacturers use some form of exhaust valve on their performance motors. Skidoo has used the rave, in bellows and computer controlled versions, since it was introduced in 89. Matched with the rotary valve it made rotax the best motor in the 80's and early 90's for sleds while everyone else was relying on "peaky" motors to make good power at the cost of them being finicky to tune for temp and altittude.
We used to mess with a guy in the shop and block one of his raves shut by cramming paper towels under the cap on one cylinder. He would cuss and fight trying to figure out why his motor wasn't running right.