Healing
Healing refers to the ability to replenish health. Healing comes from many sources, most notable being Medic. The Medic can heal any class by using his selection of Medi Guns, and pointing the beam on them, regenerating their health and providing overheal. In addition to this, healing also charges the ÜberCharge bar. While Medic is the primary healer, he is far from the only source of healing. The only thing Medic cannot heal (aside form the enemy team) are Buildings which are repaired by the Engineer's Wrench.
Medic
Medic is the primary healer, with his Mediguns healing at different rates depending on when they were last in combat. If the target was last damaged 10 seconds ago, they heal at 24hp/s. If they were last damaged 10 or 15 seconds ago, they are healed at a rate of 72hp/s. The tripled healing rate on patients who are out of combat is often referred to as crit healing. This mechanic is in place to encourage falling back to heal.
Overheal
Overhealing is an effect where the Mediguns can temporarily increase their patient's health beyond their maximum health. The maximum overheal is 150% of a patient's base health. For example a Heavy has 300 base health, and thus recieves 150 extra health with overheal, totalling to 450 health in total. For some patients with lower max health, for example a Scout, if the overheal would end with a decimal, it is rounded down. So Scout only get 185 overheal.
Overheal slowly decays with time, approximately 15 seconds, provided the person overhealed doesn't take any damage. It doesn't matter who, the overheal will decay at the same time. While a Medic can be boosted to 225 health and a Demoman is boosted to 260 health, they both decay in the same time.
ÜberCharge Building
Übercharge builds while the Medic is healing. The standard Medi Gun builds full charge in 40 seconds. However if the patient is already overhealed beyond 142.5% of their base health, the build rate is halved, this makes the charge take 80 seconds to build. This is meant to discourage pocketting (healing only one person) in favour of healing the entire team. The Kritzkrieg is different and has an increased 25% Übercharge build rate, taking only 32 seconds to fully charge, but still takes 64 seconds if pocketting someone.
Health Regeneration
Health regeneration (sometimes called health regen)is when a player recovers their health themselves. This is usually slower than a Medic's healing beam, but can be crucial to surviving fights. So far there are only 3 classes with regenerative health: Medics, Civilians and Pyros with the Harvester equipped.
Medic at based has a self-regenerating health, approximately 3 health per second. The health regeneration activates after some time in combat,and can save the Medic from burning to death. The Civilian has similar regenerative properties, but unlike the Medic he shares the health regeneration to all of his teammates who are around him. Pyros with the Harvester regenerate health when an enemy is burning and the Harvester is the active weapon at 5 health per second. This even works if the enemy is already dead. As long as they are burning, the Harvester collects.