The roach is the extra sail area added by curving an edge outward (convex) beyond a straight line between two corners, most commonly seen on the leech (aft edge) of a fore-and-aft sail. This extra material is usually supported by battens. On traditional square sails, the roach is a concave cut at the foot of the sail, designed to clear stays and other rigging when the sail is set.
Heard on the job
We need to insert the full battens to support the massive roach on that new mainsail.