General Information
Monster Heal is a monster attribute that does as it implies- it allows them to heal life back over time after avoiding injury from the hero.
The speed at which a monster regenerates its life depends on various things. Most crucially is the difficulty of the game you are playing in: in Hell, Monsters will regenerate at a much higher rate than in Normal. Another factor is their HP total- the regeneration is a % of their maximum HP- that is, to say, the more HP a monster possesses, the more HP it heals each second.
Diablo/Hellfire
Monster Heal is something not many players may know about. The only ways to really notice that such a thing exists is through one of Pepin's randomized gossip lines, or extensive use of Golem. And even then, it is generally not too big of a hinder (Or an aid, in Golem's case), because by the time such regeneration would be useful, the heroes' attack power and speed is too much.
Unfortunately, for those few who do not have that edge, Prevents Monster Heal is not available ingame, even with Hellfire installed. Equip your hero with that in mind.
Diablo II/Lord of Destruction
In Diablo II/Lord of Destruction, Monster Heal is much more of a boon (Or an aid, if its your Hireling or Summons) to the minions of Hell, because while they did not regenerate while the hero was in town in the original Diablo, they will in Diablo II, expansion enabled or not. Another factor to that regeneration is the actual monster type- that is to say, a Minion of Destruction of Nightmare Difficulty may regenerate faster than a Steel Scarab of Hell Difficulty.
But fear not, for there are a couple ways to combat that regeneration. Unlike the original Diablo, Prevents Monster Heal does exist, in an easily obtainable affix for Magic/Rare Weapons. Another method, although not so effective, is the Poison attribute, due to it being a Damage over Time (DoT) effect. And then there is Open Wounds, which does unavoidable bleeding damage over 8 seconds, scaling with your hero's level, usually many times enough to prevent the monster's regeneration.
Diablo III
Although Monster Heal in Diablo III is no longer around, before a patch, if the Nephalem fell in battle against a Champion or Unique, that monster group could heal itself to full. This frustrated too many players, however, resulting in Monster Heal being removed as of a patch. As of now, the only way a monster can heal is the Vampiric affix.