When you're alee, you're on the side of a boat facing away from the wind. If a sailor moves the sail alee, she moves it downwind.
Alee is a nautical term, one you're most likely to hear on a boat or ship. Another way to say "on the downwind side" is leeward. Both words include lee, from the Old English hleo, "shelter, cover, defense, or protection." So the alee side of a sailboat is the side that's sheltered from the wind, and the phrase "Hard alee!" is a command to move the sail to the boat's protected side.