Accelerate= speed up; in this case it speeds up the flash graphics of dealing damage and so on; you also need not confirm your opponent's playing a card - the game will autmatically proceed. Thanks, by now, the button stays pushed after you do it once. Since almost everybody will get tiered of the graphics (I think), this is a very good thing. I'd guess that without it, the points in tournaments would be vsibly lower.
In short: It accelerates the display of which card wins and which card loses.
[What I would still like is an accelerated timeout frame. Give me chess watches for a total of 1/2/3 minutes for each player to play all their cards! Would be a nice new room as well. (Timeout==instant loss) One could finally rely on being able to play a fast game.)]