1. In a bad sense, a leader of a popular faction, or of the mob: A demagogue is a political agitator who appeals to the passions and prejudices of the mob in order to obtain power or to further his or her own interests.
2. In ancient or former times, a popular leader who represented the ordinary people: It is said that a demagog acted or spoke for the uncivilised mob of people.

Two examples of demagogs in past history were Adolf Hitler and Josef Stalin.
3. Etymology: from Greek demagogos which is from demos, "the people" + agogos, "leading".