"Contra-" usually means "against," and to contradict is to go against or say the opposite of what someone else is doing or saying. Sometimes to contradict is to frustrate with words, like when one person says "The sky is blue" and another says "No, it's azure."
Denying or distorting the truth is a big part of trying to contradict. It can be harmless verbal back-and-forth, like when a husband and wife disagree just to disagree, or contradict each other to make a humorous point, but at other times people contradict something to make another person look like a liar. Often, a person who has lied will later contradict himself by saying something different from what he said earlier — and sometimes the two sides contradict each other, and neither is actually right.