A demerit is a mark for doing something wrong. Running in the hall at school might get you one demerit. Running in the hall naked could get you a demerit that will go down on your permanent record. Avoid!
A demerit is also a fault or weakness. If you're trying to decide which candidate to vote for, consider the merits and demerits of each. The other kind of demerit is a punishment — a negative mark against someone, especially a student or a member of the military. Your teacher might have a policy of handing out three demerits before requiring students to stay after school for detention. The Old French desmerite combines des-, "not," and merite, "merit," or "worth."