An outhaul is a line which is part of the running rigging of a sailboat, which is used to extend a sail, and control the shape of the curve of the foot of the sail. It runs from the clew (the back corner of the sail) to the end of the boom. The line is pulled taut to the appropriate tension (to provide the desired shape to the foot), and then secured to a cleat on the boom.
The details vary, but the two most common methods are:
The outhaul, besides simply holding the sail out, is an effective sail shape control. Tightening or slackening the outhaul can flatten or fill out the sail, shift the draft forward or aft, change leech and foot tension, increase or decrease camber.