Healing spells are far more common in the 5e rules set than older editions. Some of these spells can be used during combat. Characters who use up all their hit points remain at zero points until either: a. They lose their death save and die, b. are stabilized, or c. are healed. Healed characters (even one point!) are able to fully function in combat again. This leads to what is sometimes call the "whack-a-mole" effect, where downed characters keep popping up again.
To create more balanced, exhaustion rules are added to downed characters who are healed in combat. If a character who has fallen to zero hit points and is healed before dying, that characters receives 1 exhaustion level (PH p.291).
Some effects can remove exhaustion. A long rest (plus food and drink) will remove one level of exhaustion.