To subdue is to hold back, put down, or defeat. A Doberman can be subdued with a bone, but subduing a yapping toy poodle can be a mail carrier's greatest daily challenge.
You can use the verb subdue in ways ranging from subtle to very forceful. If someone is angry, you might subdue him with kind words that overcome his anger. If someone is coming at you with a giant karate chop, you may be able to subdue her with a secret weapon — a knee-snap–heel-kick-floor-drop. Sub-, as in submarine means "below" and subdue means to bring low — to keep down literally or to calm down emotionally.