Non-Federation was a term used to refer to species and planets which were not members of the United Federation of Planets. It could also refer to worlds, such as Earth, prior to their joining the Federation.
In 2369, there were seventeen people from non-Federation planets aboard the USS Enterprise-D. (TNG: "The Chase")
As late as 2371, non-Federation citizens needed a letter of reference from a command level officer before they could take the entrance exam for Starfleet Academy. (DS9: "Heart of Stone")
Aboard the USS Voyager, Neelix and Seven of Nine only found references to Shannon O'Donnel by having the ship's computer expand the record search to include non-Federation databases. (VOY: "11:59")