In Pokémon Black & White, as usual, you get a number of storage boxes within which you can store a variety of Pokémon through the PC in Pokémon Centres, the Battle Subway and various other areas. In Black & White, you start out with a simple system containing 8 boxes. Each box can store 30 Pokémon allowing for up to 240 Pokémon to be stored within. However, this is by no means enough to store all the Pokémon around.
This system can be enhanced by simply putting a Pokémon in each of the boxes. Once you have at least one Pokémon in each of the 8 boxes, when you next access the PC, you will suddenly have a further 8 boxes bringing the total up to 16 so you can store 480 Pokémon. To increase it once again, place a Pokémon in each of these boxes and you'll get the final upgrade up to 24 boxes capable of holding 720 Pokémon. This allows you to store at least one of each Pokémon with plenty of room for extras.