When you express disbelief, you make it clear that you don't believe something is real or true. Your reaction to your little brother's stories about fairies is likely to be disbelief.
You'll probably encounter a lot of disbelief if you go around telling everyone you saw a UFO. You'll feel a sense of disbelief yourself if you learn you've won the lottery. In both cases, it just doesn't seem possible or real. The belief part of disbelief comes from the Old English word geleafa, "belief or faith," which evolved into bileave before becoming belief. The prefix dis- means "not" or "the opposite of."