It normalizes the volumes of all the songs to a common level, eliminating (or helping to reduce) volume inconsistencies between tracks. For example, my "The Wall" album seems to play at a lower volume than the rest of my tracks. Turning on "Sound Check" on the iPod helps to bring the volume of that album up to be more "equal" to the rest of the tracks.
I know in iTunes, songs are scanned for their volume -- I'm not sure exactly how it works on the iPod, since there's no scanning when the option is enabled. Some people on ipodlounge.com seem to think that Sound Check has to be enabled in iTunes before it'll work on the iPod, but I've got it disabled in iTunes and enabled on the iPod, and it seems to work fine. Maybe it just works "better" if it's enabled in both iTunes and on the iPod.