an Xbox modification to the harddrive, which allows for extra functionality, including running games from the hard drive, faster read times, upgraded dashboard, Internet surfing, and music /movie playback capability (mpegs, avi's, wav's, even Xvid)
A softmod is the act of using software to modify hardware such as a video card or sound card in a way that can unlock or enable disabled features, usually pipelines. Cards that can be modified using software to faster versions (without regard to clock speed) usually contain much of the same hardware. Softmodding a card should not include changing the video card's bios, as that's considered a bios flash.