A Dream Ball allows you to catch Pokemon that you have met in the Dream World. It "appears out of nowhere" it your Bag and can only be found in the Entralink. Here's a picture:
It has a 255x catch rate, the same as a Master Ball.
This website allows access to the Pokemon Global Link, which can be used to access the Dream World. You'll need a copy of Black, White, Black 2 or White 2 which is connected to the internet.