First aid is a subset of medicinal skills meant to save lives. The primary function of first aid is to prevent fatal bleeding and critical issues that need to be dealt with immediately. It can be applying a tourniquet on a heavy bleed, set a broken bone right, restore a dislocated joint, dealing with severe inflammation etc. First aid can only be used directly after someone has been injured, not as an ongoing thing. If you need to treat someone who is injured and recovering, use Medicine instead.
First aid immediately recovers a person from Down and Out and removes one Wound from a character if used as part of a Rally action. If the check fails, no Wound is recovered, but the character is still recovered from Down and Out.