Answer:
Exactly that ... accidental death (not from natural causes). As for dismemberment, some policies allow partial compensation for losing a foot or a hand, or maybe for an eye.
Having stated the above, please bear in mind that this is not a blanket answer that will apply to each and every AD&D insurance coverage. Different insurance plans may vary on what is covered and how much the compensation will or will not actually be. In all cases, consult your insurance carrier for the 'official' word.