Regeneration is a property that speeds the recovery of HP drastically; your character gains 1 HP on every turn (s)he would not normally do so.

It is acquired as an extrinsic through putting on a ring of regeneration or wielding the Healer's quest artifact, the Staff of Aesculapius. It can only be acquired as an intrinsic by eating a ring of regeneration if the ring is of suitable material and you are polymorphed in to a monster that can eat it.

The downside to having faster regeneration however, is if the property is from a ring, either eaten or worn, you lose an additional point of nutrition every other turn.

More details on the effect of regeneration on hp recovery can be found at Hit point regeneration.

Also, some monsters have regeneration, e. g. vampires and vampire lords, werecreatures, all trolls, all liches, archons, and the Wizard of Yendor.