Loss of quality by stages rather than all at once. Graceful degradation means less is offered rather than nothing.
Medieval Latin degradatio (a reduction in rank), from degradare (to reduce in rank), from de- (down) + gradus (step, rank); loss of quality taken down by stages rather than all at once, one step lost at a time.
Its root, gradus, is a rank on a ladder, and degradation was first about falling a rung, not falling off entirely. A system built to degrade gracefully loses rank one step at a time, never all its rungs at once.