Life Regeneration (also stated as Life per Second) is one of the healing stats in Diablo III which grants a passive, fixed recovery of Life over time. It is equivalent to Replenish Life from Diablo II, although it is much easier to acquire than in the previous game.
Characters start with little to no Life Regeneration. It must be obtained from items, skills, or Paragon points. A character heals the fixed amount of Life every second (technically every 0.25 seconds, with numbers popping up every 0.5 seconds), summed from all sources, regardless of whether or not the character is in combat and under attack.
Life Regeneration is a Primary attribute on items. 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 non-Ancient items is 79236 (86914 with the Hamburger, plus another 40000 from Boots of Disregard, plus the Molten Wildebeest's Gizzard bonus). With Ancient Legendary bonuses, it can go up to 113110.
Two Sets increase Life Regeneration as well when assembled: Captain Crimson's Trimmings (+6000) and Guardian's Jeopardy (+8000).
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 far more effective when the character has high resistances and armor; all these stats synergize to calculate overall Recovery.