Luff

The luff is the forward edge: on a mainsail it runs up the mast, on a headsail up the forestay or a furler, and on a spinnaker it flies free (and swaps sides every time you gybe — on a symmetric kite, whichever edge is forward is the luff at that moment).

Its length is usually the first measurement anyone asks for, because it sets the sail's height. It is rarely a straight line: a mainsail's luff is cut with a deliberate outward curve, and pushing that extra cloth against a straight mast is what puts belly into the sail. See luff round.

If your sail's luff has stretched, the sail gets deeper and more powerful in exactly the wrong conditions. That is one of the classic reasons a sail ends up on the recut table.