Life Regeneration (also known as Life per Second or Replenish Life) is one of the healing stats in Diablo II and Diablo III. Unlike Life Steal and Life on Hit, it offers a passive, fixed recovery of Life over time.
Originally, characters have little to no Life Regeneration.
In Diablo II, this was an uncommon affix: to get an effect comparable to a potion, players would need to stack it on every slot. However, it provided a good source of healing when outside combat or for the ranged attackers.
In Diablo III, Life Regeneration is a Primary affix roll. It heals the fixed amount of Life every second (technically every 0.25 seconds, with numbers popping up every 0.5 seconds), regardless of whether or not the character is in combat and under attack.
It may appear on any non-weapon piece of gear, rolling up to 7678 at level 70 on Helms, Rings, Bracers, Gloves and Amulets, and up to 5528 on all other types of Armor and off-hand items. The only weapon that can roll Life per Second is The Horadric Hamburger (also up to 7678). Up to 10730 (214.6 per point) Life Regeneration may be obtained from Paragon levels, in the Defensive section.
Total amount of Life per Second a character may legitimately obtain from items is 79236 (86914 with the Hamburger, plus another 40000 from Boots of Disregard, plus the Molten Wildebeest's Gizzard bonus); with the Ancient Legendary bonuses, it can go up to 113110.
Some skills, like Inspiring Presence or Brooding, add a bonus to Life Regeneration based on the maximum amount of Life. For obvious reasons, Life per Second is way more effective when the character has high resistances and armor and low maximum Life.