On a rapier or Italian grip fencing blade, the ricasso is the unsharpened section of the blade between the foremost part of the guard and the quillons. On a rapier with a swept or cup hilt (see here for a nicely labelled example of a swept hilt), the quillons sit immediately in front of the grip, and the cup or several bars of the guard extend an inch or two in front of the crosspiece. This part of the blade typically has a rectangular cross-section (rather than diamond-shaped or oval like the rest of the blade). It allows the user to curl one or two fingers around in front of the quillons, which has a couple advantages. It gives the wielder a better hold on the grip, preventing it from twisting in the hand, and moves the hand closer to the balance point, which makes the sword feel lighter.