its the time you have to move. 3/2 means you get 3 min to play the whole game, but every move you get 2 more seconds. so if you make 10 moves very quickly, say in 5 sec in the opening, you have 3 min and 20 seconds total play time and 3 min 15 left for the rest of the game. This one is, then, a very fast paced competition.
10/0 is 10 min for all your moves, period. Games last up to 20 min, usually 10-15 per game.
Is there anywhere on the site a guide to all different type of tournaments? I don't understand what the names mean, 3/2, 10/0, etc...