Regenerate is an activated ability that protects a permanent (in most cases a creature) from being destroyed or taking lethal damage once. Instead of sending the card to the graveyard, all damage is removed and the card is tapped and removed from combat.
To prevent a creature from being destroyed, a regeneration effect works like a shield. If a creature would be destroyed and it has a regeneration shield, it's not destroyed. Instead, the creature becomes tapped, it's removed from combat (if it's attacking or blocking), and all damage is removed from it. That regeneration shield is then used up. The creature never leaves the battlefield, so any Auras, Equipment, or counters that were on it remain there. Any unused regeneration shields go away during the cleanup step.
Regenerate can mostly be found on or cards.
701.13a If the effect of a resolving spell or ability regenerates a permanent, it creates a replacement effect that protects the permanent the next time it would be destroyed this turn. In this case, “Regenerate [permanent]” means “The next time [permanent] would be destroyed this turn, instead remove all damage marked on it and tap it. If it’s an attacking or blocking creature, remove it from combat.”
701.13b If the effect of a static ability regenerates a permanent, it replaces destruction with an alternate effect each time that permanent would be destroyed. In this case, “Regenerate [permanent]” means “Instead remove all damage marked on [permanent] and tap it. If it’s an attacking or blocking creature, remove it from combat.”
701.13c Neither activating an ability that creates a regeneration shield nor casting a spell that creates a regeneration shield is the same as regenerating a permanent. Effects that say that a permanent can’t be regenerated don’t prevent such abilities from being activated or such spells from being cast; rather, they prevent regeneration shields from having any effect.
|Birthing Hulk (7)|
Creature — Eldrazi Drone (5/4)
Devoid (This card has no color.)
When Birthing Hulk enters the battlefield, create two 1/1 colorless Eldrazi Scion creature tokens. They have "Sacrifice this creature: Add to your mana pool." ( represents colorless mana.)
|Consecrated by Blood (4)|
Enchantment — Aura
Enchanted creature gets +2/+2 and has flying and "Sacrifice two other creatures: Regenerate this creature." (The next time the creature would be destroyed this turn, it isn't. Instead tap it, remove all damage from it, and remove it from combat.)
|Cruel Revival (5)|
Destroy target non-Zombie creature. It can't be regenerated. Return up to one target Zombie card from your graveyard to your hand.
|Flesh to Dust (5)|
Destroy target creature. It can't be regenerated.
Destroy target creature with power 4 or greater. It can't be regenerated.
Creature — Eldrazi Drone (4/3)
Devoid (This card has no color.)
Skitterskin can't block.
|Undercity Troll (2)|
Creature — Troll (2/2)
Renown 1 (When this creature deals combat damage to a player, if it isn't renowned, put a +1/+1 counter on it and it becomes renowned.)
: Regenerate Undercity Troll. (The next time this creature would be destroyed this turn, it isn't. Instead tap it, remove all damage from it, and remove it from combat.)