Convergent thinking is the application of knowledge you already have to a clearly defined question. There is not much creativity involved, but more pulling information you already have stored in your mind and reciting it. Questions requiring convergent thinking include "what is 3 times 3?" and "Is a cat a mammal?"
Divergent thinking is the synthesis of new ideas, and involves solving a problem without already having the information. This type of thinking involves creativity. Problems include figuring out how to make your roommates couch fit through a door, or designing a rollercoaster in Rollercoaster Tycoon.
It's worth noting that creativity usually involves a bit of both thinking processes, since you usually have to draw from preexisting knowledge in order to solve an unfamiliar problem.