The zero range is the range that a firearm is sighted at. For example if you are shooting a rifle with a scope that is sighted in at 200 yards that means that if you want to shoot a target that is 200 yards away you should place the crosshair dead center on the target, because that is the range it is zeroed at. For firearms with iron sights the zero range usually refers to the range where the bullet hits the center of a target if you align the sights up.
You want to zero in your firearm usually at the distance of the objects you will be shooting at. Also it is common to zero in a firearm at its maximum point blank range.
For pistols a typical zero is 25ft
For hunting rifles a typical zero can be 100 or 200 yards.