Pokémon Black and White versions

what's all this dream business in b/w?

The Dream World is an online thing where you can upload a Pokemon from in-game and play mini-games and befriend other Pokemon with it.
To access the Dream World, afaik, you have to have a Munna or a Musharna and talk to one of the Professor's assistants and you gain access to it.
Pokemon you befriend in the Dream World will eventually challenge you and give you a chance to capture them, and Pokemon that you catch from the Dream World have abilities they don't normally have, such as Vaporeon having Hydration instead of Water Absorb and etc.