Couple of things wrong here, but mostly right. AF-S means that it has an autofocus motor built into the lens ("S" standing for silent wave). AF-S lenses can be used on the majority of contemporary Nikon SLRs. It is like Canon's USM (Ultra Sonic Motor). All other Nikon AF lenses (except for AF-I, "I" meaning internal) do not have autofocus motors built into the lens and operate off of a screwdrive that the camera itself operates. All Nikon SLRs have this screwdrive thing except for the D40/x. What darich is getting at about how you can't use it on digital are the DX-series lenses that are made for the DX sensors in Nikon DSLRs (like Canon's EF/EF-S where EF-S is for 1.6x crop sensors/bodies). Theoretically you can use a DX lens on a Nikon FF SLR, but you run risk of the mirror cracking on the back of the lens while installed, and/or circular vignetting. I've tried it on my secondary film SLR (a N6006) and had the latter effect.
The crop factor on Nikon DSLRs (atleast the majority of them... specifically the D80 in question) is 1.5x, that's what the DX thing is about. At this date, Nikon doesn't sell a FF DSLR although there has been talk that the D3 series may have a FF sensor.
Hope you enjoy your D80!