'Absorb' was introduced in the Time Spiral block and it currently appears on only one card: Lymph Sliver.

702.61. Absorb

• 702.61a. Absorb is a static ability. "Absorb N" means "If a source would deal damage to this creature, prevent N of that damage."
• 702.61b. Each absorb ability can prevent only N damage from any one source at any one time. It will apply separately to damage from other sources, or to damage dealt by the same source at a different time.
• 702.61c. If an object has multiple instances of absorb, each applies separately.

Translation:

• 702.61a - Absorb is always active and being checked, it is not triggered in response to damage being dealt to the creature.
• 702.61b - This is the real programming of the card, it prevents N damage from any single source. If the Lymph Sliver is a 2/2 with Absorb 2, a Lightning Helix deals 1 damage to the Sliver but a Shock played at the same time will not deal any damage to it.
• 702.61c - Absorbs stack. So if you have two Lymph Slivers in play, your Slivers have 2 instances of Absorb.