Draining is an effect that weapons with the draining brand, certain spells, and certain monsters can inflict with their attacks. A player who has been drained will lose experience (roughly 10-20% of the amount needed to get to the next level) and possibly levels (your skills will not be affected), while monsters will have their HD reduced, lowering their max HP and making all of their abilities noticeably weaker. If a player should somehow manage to still have positive HP after being drained of all experience, or if a monster should survive being reduced to 0 HD, they will immediately die. As such, encountering monsters armed with draining weapons on D:1 can be surprisingly fatal.
Each rank of life protection reduces the experience lost by 1/3. The undead, plants, and demons possess full protection innately, while the living must find other means.
While drained enemies are significantly easier to defeat, they also give you less experience for defeating. However, this effect is very small and should mostly be ignored in your decisions. One especially good target for draining attacks are shapeshifters. The forms these monsters can assume vary depending on their current HD. Draining their HD leaves them with a much less deadly set of options.
Strangely enough, eyes of draining do not in fact have any experience draining abilities. Instead, they drain your MP.