The concept of regenerating health is very simple: instead of requiring the player to find med kits to recover their health from injuries, the player's wounds will automatically heal if they can avoid taking any more damage for a set amount of time. This allows the player to be in top condition at the beginning of every skirmish, and lets them play the game on a battle-by-battle basis.
The origins of the recharging health mechanic date back to action role-playing games, or action RPGs, of the 1980s. The first video game to use a form of regenerating health was Punch-Out in 1983. In 1984, Hydlide introduced the regenerating health mechanic in a more modern form, where the player escapes damage for a set amount of time in order to recover health. This mechanic then went on to appear in the popular Ys series from 1987 onwards. The first shooter with the mechanic was Star Luster for the NES in 1985. However, this mechanic was rarely used outside of the action RPG genre until the 2000s.
Halo: Combat Evolved is sometimes credited for the first appearance of regenerating health in FPS action games. However, not only was it not the first, but it did not even have regenerating health. Halo featured a traditional health system, as it was the player's energy shields that regenerated. Subsequent games in the series, starting with Halo 2, added true regenerating health, although the original system made a return appearance in Halo 3: ODST and continued on in Halo: Reach.
In truth, this popular method of health control appeared in action games long before Halo. The 1992 first-person shooter Faceball 2000 for the SNES and Mega Drive/Genesis had it. It also was used in the relatively unpopular comic book game, Wolverine: Adamantium Rage, which was released on the SNES and the Mega Drive/Genesis in 1994.
Types of Regenerating Health
There have been multiple types of regenerating health.
Some games have a health bar like normal and is depleted like normal, but when in critical condition your health will regenerate which will then stop at a certain point. Once this has happened you must grab a health pack to continue any further in your healing process. Prey is an example of this style; if your health is lowered to below 25%, it will regenerate back to 25% and then stop.
Others use segmented health bars, which will regenerate up to the next segment. Resistance: Fall of Man is an example of this style, with the player's health regenerating up to 25%, 50%, 75%, or 100%, depending on which segment their health was lowered into. Again, health items can be used to restore the lost portions.
Another kind of game will have no segmentation and your entire life supply regenerates. This means when walking around in non-combat areas you are always at full health. These games have no need of health pickups, and often do not even show a health bar of any kind. In such cases, your closeness to death is mostly determined by indications of your character's pain, causing any combination of blurriness, red coloration, de-saturation, and audio muffling. Since the player is already at the brink of death and typically in an intense situation when these audiovisual impairments occur, they often serve to seal the player's fate. The Call of Duty series is perhaps the most well-known example of this mechanic.
There are, of course, singular examples which don't quite fit into any of the above categories. In Just Cause 2, for example, the player's health will always regenerate a set amount from the point at which they stopped taking damage; whether this leaves them barely hanging on to life or fully healed depends on when they manage to get to cover, similarly to the segmented style. However, med kits will always fully heal their bar the rest of the way, acting similarly to the Prey-like style.