From Texas Standard:
After the Sandy Hook shooting, President Obama and his colleagues in Congress pushed to close what they call a loophole in background checks. They were not successful. The word loophole, it should be noted, is a political term, primarily used by advocates of gun control who say there's a gap in the law when it comes to the sale or transfer of guns between private citizens.
Under existing law, anyone who's in the business of buying or selling guns is supposed to have a federal firearms license. If you have a federal firearms license, then you have to have to run a background check on any gun transfer. But at gun shows, not everyone selling guns is in the regular business of selling them, and not all sellers have to run background checks. Neither do people selling online.