You most likely will only encounter a J64 file if you are looking to play an Atari Jaguar game on your computer or mobile device using an emulator. There are several emulators available for playing Atari Jaguar games, including MAME, RetroArch, and Phoenix.
The Atari Jaguar was a 64-bit video game console released in 1993. It was a commercial failure and helped put Atari out of the home video game console market.
The console has since gained a cult following, which has led to the rise in emulators supporting Atari Jaguar games.
NOTE: Atari Jaguar games may also be dumped to .JAG files.