In previous generations, when you used some specific moves after other ones, some got a boost. An example of this would be using Roll Out after using Defense Curl. However, in Pokémon Black & White, the Combination Moves get taken up a further level.

Functionality

In Black & White, the Combination Moves are done by using two seperate moves with two of your Pokémon during Double or Triple battles. These moves will then combine and have an added extra effect. These effects vary from simple status afflictions to doing damage to the Pokémon.

Grass Pledge + Fire Pledge

Moves Required: Grass Pledge & Fire Pledge

Effect:
When you use the move Grass Pledge and then the move Fire Pledge during a Double or Triple battle, the move will combine and create a field of fire which causes small amounts of damage to your opponents each turn.
Fire Pledge + Water Pledge

Moves Required: Fire Pledge & Water Pledge

Effect:
When you use the move Fire Pledge and then the move Water Pledge during a Double or Triple battle, the move will combine and create a a rainbow over the battle area. This move increases the likelihood that any secondary effects will occur when your Pokémon use moves.
Water Pledge + Grass Pledge

Moves Required: Water Pledge & Grass Pledge

Effect:
When you use the move Water Pledge and then the move Grass Pledge during a Double or Triple battle, the move will combine and turn the field into a swampy moor style area which lowers the speed of your opponent's Pokémon.