Why the "up" in "hang up the phone"?

Do a google image search for "old time phone" and I think you will understand a little better. Once upon a time, the phone had little U shaped hook on the side, and the ear piece rested there while not in use. Also, this hook connected to a switch inside the phone, and the weight of the ear piece was needed to close this switch and disconnect the phone. So the expression at that time was almost literal, the user of the phone needed to hang the ear piece up on the hook, lest it dangle like a pendulum from its cord. Today, we keep the expression out of either habit or tradition.

EDIT: Not totally related, but it suddenly occurs to me, that we also still dial our phones, even thought the pulse rotary system was dead by the late 1980s.

The word up can mean to transition to a state in which something is completed. For example, "your time is up". When you "hang up" the phone, you transition it into a state in which something is completed, just as when you "clean up" your room or "give up" in a contest.