The term 'oxymoron' is generally used when talking about literature to explain a phrase that is completely contradictory, for example "the loud silence" (or something more poetic). From the Greek for 'sharp/clever' (oxys) and 'dull/stupid' (moros), which makes the word an oxymoron in itself... I don't know how often you'd get to use it in everyday speech, most people would just say 'contradiction', 'contradiction in terms' or something similar. As I said, oxymoron is really a literary term, you would use it when describing how a writer creates a certain effect. Have I helped at all?!

Sometimes people also use the word sarcastically, for example one might say "An honest politician - that's an oxymoron!" to emphasize how completely different a noun is from its adjective (in this case, the person would be saying that politicians are far from honest.)