To shut down, or threaten with legal action, a website or other creative fan project under the guise of copyright infringement.
The term arose, of course, from Twentieth-Century Fox, a media company which has a history of overzealous protection of intellectual property rights, especially as regards the Web. This apparently started around late 1996, when fansites for such Fox shows as The Simpsons and Millennium began to receive letters from the company's law firm, demanding the removal of any images, sounds, or other material copyrighted to Fox. In some cases, rather than contacting the webmaster, the lawyers went directly to the sites' web hosting providers, many of whom deleted entire web pages before their designers knew what had happened.
But it wasn't over: other derivative works by fans got foxed in early 1997: for instance, managers for Oasis threatened many of the band's fansites, and an add-on package for the video game Quake based on the Alien films (owned, naturally, by Fox) was shut down. Since then, other companies have tried the same strategy, perhaps trying to protest their financial interest in their own copyrights and trademarks. A few, however, have chosen to enforce their rights more loosely in the interest of perserving amity with their own fanbase, such as the Lucasfilm/LucasArts family (witness the popularity of Kevin Rubio's Troops and other Star Wars fan films).
Sources: www.bringers.org.uk, www.planetquake.com, whatis.techtarget.com.