EB0 (known as Mother in Japan,) is an RPG that takes place in America in the 1980's. Unlike most RPG's is modern instead of midevil. Strange occurinces begin to happen, and a boy who sets out to investigate these along with some mysteries of his past. He is joined by several friends who help him with his final goal, which is defeating the evil alien Giegue.
EB0's four main characters are Ninten, Ana, Loid, and Teddy. The first three look a lot like the first three main characters in EarthBound for the SNES, but there seems to be no connection between the two games. There are a lot of other simmalarities though.
Nintendo translated the game to English, but never released the game. In 1998, a group of ROM translators discovered that Nintendo had auctioned off a prototype of the EarthBound 0 cartridge. They contacted the individual who had the game, and made an agreement to borrow the game for a few hundred dollars so they could dump the cartridge to a ROM file. That's how we can play EarthBound 0.
EarthBound 0 was originally called EarthBound, but since the sequel for it was realised in North-America as EarthBound, it has been dubbed 'EarthBound 0'.