Felonies are more serious crimes that carry much higher penalties (jail term) than misdemeanor. In states like Texas, California, Washington and several others that have the 3 strikes law, persons convicted of a felony who have been previously convicted of two or more violent crimes or serious felonies usually receive a life sentence.
For example, murder or armed robbery are felonies while shoplifting is a misdemeanor. In several states, possession of small amounts of marijuana has been downgraded to a misdemeanor. The penalty for misdemeanors often involve only a fine and no jail term. If a jail term has been ordered, it is usually less than 1 year.
edit Video explaining the difference