Leech line stops flutter
One of the most important purposes of the leech line is to stop the leech from fluttering. Usually, you want as flat a leech as possible, without it fluttering. As the sail ages and stretches it will have more of a tendency to flutter, which rapidly accelerates wear. Tighten the leech line just until that fluttering stops. Top quality sails may well have a similar line in the foot of any headsails or in a loose-footed mainsail.By the way, before you adjust the leechline on your headsail, make sure your jib leads are correctly positioned. If they are too far aft (usually when running), there will be too much twist in the sail. The head will fall off too much and the leech will flutter, or maybe the whole head of the sail will be luffing slightly. It is easy to miss this, since your view of the head of the jib is obscured by the mainsail, but this can really age your sail, not to mention affect your boatspeed.