Belief, in simplest terms, is what the mind accepts as true. One can believe something to be true without having knowledge that it is true. Also, one can believe something to varying degrees of certainty (see also Probability).
Believing something without evidence is called faith. "Belief" does not always imply "faith," as one can believe something based on evidence. For example, one does not have faith that the sun will rise tomorrow, since the fact that the sun rises every day is supported by a lifetime of personal experience, thousands of years worth of recorded observation, and a scientific model of the earth's rotation.