Federal Firearms License. Basically someone/an entity legally allowed to sell guns to the public. Usually a gun retailer (i.e. your local Bass Pro or some smaller gun store). In some smaller communities out here, you’ll find other people that have them as well. For instance, a friend of mine from college owns a boat dealership in a pretty rural area, but he has a FFL just to help with transfers (they charge a fee, and there aren’t a ton of other places with a FFL within 75 miles).
Anyhow, the idea is that if you were to buy a weapon (say online) from a private individual, they would send that weapon to a FFL holder in your state, after which you could go to the FFL holder, fill out some paper work, pay a transfer fee, then take the weapon.