Healing Surge
The Healing Surge is a game mechanic introduced in Dungeons & Dragons 4th Edition as part of the overall revamp about healing and the Hit Point system.
In summary? Healing surges denominate the amount of "spare life force" that a PC or NPC has available at the start of each day. As most healing powers work along the lines of "spend a healing surge and regain healing surge value + x hit points", this affects how often a character can heal themselves each day and gives incentive to not be too careless with their health.
Healing surge value, incidentally, is rulespeak for "one quarter of your maximum hit points (rounding down)".
PCs have healing surges to spend equal to their class level + their Constitution modifier - squishy classes like the Wizard or the Warlock tend to get fewer healing surges, as per the tradition, but the difference isn't as major as you might think. For example, in the first PHB, the Defenders (Paladin and Fighter) have 10 and 9 healing surges, respectively, whilst the Leaders (Warlord and Cleric) have 7 healing surges and the Wizard and Strikers (Ranger, Rogue, Warlock) have only 6 each.
Though universal in 4e, it was abandoned as such in Dungeons & Dragons 5th Edition, although the 5e Fighter still retains an analogue mechanic as part of its defining class system.