This term has two separate but related meanings. The first is the way fabric hangs or falls. Heavier fabrics generally drape more attractively than lighter ones, but different fabrics drape differently - compare silk to linen.
The second meaning is specific to formal jackets and is both elusive and controversial; it refers to the amount of loose fabric in the chest and behind the shoulders, and particularly to a fold of cloth that runs vertically on the outer edge of the chest. The point of this is to accentuate the contrast between the width of the chest and the narrowness of the waist. The alternative to a suit cut with drape is a very clean chest, which is currently the prevailing fashion.