Cast-off (for a right hander) is the amount of "cast" or "bend" in the centre-line of the stock as compared to the centre-line of the barrel. Imagine a straight line running down the centre of the barrel (or rib) straight back fron the front sight or bead, over the rear of the stock. If there is no divergence between this line and the centre-line of the stock. the stock is said to be straightr, or having no cast ( when viewed from the top) If however, the centre line of the barrels is to the left of the centre line of the stock ( or vice-versa, the stock centre line is to the right of the barrel line) then the gun is said to be cast-off ... for a right handed person. The purpose of cast-off is to more precisely place your right eye in better alignment with the centre of the barrel ... making you "look where the gun is shooting". The vast majority of American made shotguns are straight , i.e., no cast, while the vast majority of quality European guns have cast-off. Personally, having a bit of a wide face, I like about 3/8" of cast-off measured at the heel on all of my shotguns. When I mount the gun, my eye is right down the middle. Without cast, it seems the centre bead is always to the right of the front bead on a gun without cast. Invariably, most right-handed shooters (right master eye) benefit from a degree of cast-off. Not so noticeable perhaps if you pre-mount a gun - as is typical in trap .or skeet - you have time to adjust your sight picture down the barrel ... but in sporting and five-stand, and certainly in game shooting, cast is beneficial to quick gun mounting ... and hitting the target. Lots of good articles on gun fitting in the various magazines like "Sporting Clays" and "Shotgun Sports". Go to a busy Gun Club and ask one of the local "Pros" - most can't resist from giving an opinion.
Interesting to see Beretta & Benelli autoloaders now coming with stock shims to adjust the amount of drop & cast !