To heal in any RPG is to restore lost "hit points" or life. It usually involves magical spells or similar effects, such as short periods of time or eating supposedly non-magical food to increase
Healing Spells
In many RPGs there are dedicated caster classes for healing, and they are traditionally not overly popular. In Diablo II, there were a few classes with some sort of "heal other" spells, but not overly efficient. No class in Diablo II is a dedicated healing class. The popular MMORPG World of WarCraft has several classes that can specialise into healing, but they can also generally specialise into something else, like DPS or tanking.
Some monsters are known to heal their own kin as well.
Other Sources of Healing
Both Diablo I and II have an extensive potion system, and the main source of healing wither come from regen, lifesteal or potions. There are also shrines which can heal you, and add quick life regeneration for a period of time.
In Diablo III there will be less use of potions, and higher use of Health Globes. Balls of health dropped randomly by monsters and which increases life. Heal potions , Minor Heal potions and Rejuvenation Potions returned to Diablo III, but at a less drop rate. These should be kept in your inventory for emergency situations against a boss when a Health globe hasn't dropped.
Heal Potions increase health slowly over time, while Rejuvenation potions heal instantly.
Another source of healing in Diablo II was to visit the nearest town to talk to the potion vendor for an instantaneous full health effect.