Cognitive biases are bugs in our mental software, that cause us to behave irrationally. I mean, we behave irrationally for all sorts of reasons, but these are some.
I've not found a good way to use cognitive biases in the design process, except to use them as stimulus for idea generation.
One of the tricky aspects of biases for design is that you don't know which if any biases are/could be affecting someone's behaviour. Therefore, it's more than usually important to test any designs using these rigorously.
List of biases
Predictably Irrational, by Dan Ariely
Nudge, by Thaler and Sunstein