A fan project is an unofficial project set in the vein of a franchise created by fans of the series. Generally, fan projects are unauthorized by the creators of the franchise. Fan projects can range from games to movies to artwork to frameworks to create fan made material.
For example, Final Fantasy: Blackmoon Prophecy is a fan-made game based on the Final Fantasy series.
Popular game series for creating fan projects include the Final Fantasy series and the Pokémon series due to Pokémon Essentials.