Level 1 - Use health kits 75% faster.
Level 2 - Use health kits 75% faster and can heal injured teammates. When looking at an injured teammate and you are adjacent to them, you can hold X to slowly heal them. 10 HP every 2 seconds.
Level 3 - Use health kits 75% faster and can heal injured teammates. When looking at an injured teammate and you are adjacent to them, you can hold X to slowly heal them. 20 HP every 2 seconds.
The level 1 version comes in handy if one is forced to heal during a firefight. Healing leaves the player vulnerable, so cutting down on the time required can greatly improve survival chances.
The level 2 version awards 20 parts for every 2 seconds of healing; the level 3 version awards 40 parts, instead. Thus, the level 2 and level 3 versions of the skill grant the same amount of parts per unit of health healed; the difference lies only in the speed of healing. Healing teammates allows them to stay in fights longer without having to use and look for health kits, and decreases their chances of being downed. While the difference may seem marginal, it can mean the difference between saving a teammate and having them downed, leaving the rest of the team more vulnerable. Regardless of level 2 or 3, the rest of the rules still apply: if less than the maximum amount of HP possible is healed, then the healer is still awarded full parts; multiple people can heal one target at once.
The higher levels of First-Aid Training work well in tandem with the reviver skill, as recently revived teammates always require healing.
It is possible to heal someone as they are taking damage. This can drastically increase their chances of winning firefights, as opponents need to generally expend more ammunition to achieve a down. Having teammates take damage from passive sources of damage, such as the flaming remains of a molotov explosion, can be an easy way to acquire a few extra parts.
Attempting to heal someone while they're using a health kit results in the player character going through the animation of healing, but without actually healing the target. The player is still rewarded parts equivalent to healing once after the target has finished using a health kit, but only if no one else was attempting to heal said target. The target of the healing is only notified that someone else is trying to heal them the instant they are done using a first aid kit.
Reviver and especially its upgraded variants work well with First Aid Training. Revived teammates come back with their health only partially replenished, and First Aid Training brings them back into fighting condition. First Aid Training is an excellent counter, as healing (either oneself or a teammate who is wounded by a crossbow) stops the crossbow's bleeding effect.