Field Medic is a very important stat that directly influences a characters effectiveness at healing and the use of First Aid Kits, Splint Kits, and other medical supplies. It also determines how effective you are using the advanced types of these items.
According to the ingame stats menu, the Field Medic skill is defined as
"This skill saves lives and allows you to stop bleeding wounds and jury-rig critical injuries, allowing characters to continue fighting when they shouldn't. In the long-term however, major injuries require bed rest. A beginner will not only heal wounds more slowly, but will use up all their medkits really quickly.
Performing first aid or operating the Medical Workbench will level up a character's Field Medic stat.