Triple Battles are only available in Pokémon White Version but you could find one or two in Pokémon Black Version. You will be able to find one or two Rotation Battles in Pokémon White Version but they are mainly in Pokémon Black Version.
Triple Battles are battles where the first three Pokémon in your party are out to battle at the same time which is quite cool. Here's a recommendation for your first three Pokémon after you've finished the main story: Zekrom(Reshiram in Black)Level 70, Emboar/Serperior/Samurott Level 75, Kyurem Level 60-70. But that's only a recommendation. When you lose one of the three Pokémon, you have to replace it with another Pokémon. When you win, all three Pokémon get the experience. Also if, for example, Zekrom uses Fusion Blast on a Pokémon and Kyurem aims for the same Pokémon, Kyurem will just attack the next Pokémon along the line.