I'm not an expert but basically the Divines are the Gods of Order and as such they are all benevolent, they gave up much of themselves in order to create the world and the people who dwell within it.
Daedra are often more associated with chaos or disorder and they often see humans as mere pawns in order to further their own wants. They are the Gods who didn't take any part in the creation of the world and as such they can communicate far more directly then the Aedra(divines).
They are both Gods, but the Daedra are much more similiar to mortals in their wants whereas the Divines are far more transedental and prone to give their followers what they need, rather than what they might think they want.