Ambaróna was one of the names of the Fangorn Forest. It was a name used in the Elder Days, when most of Middle-earth was covered in forests. Fangorn formed the eastern end of those.
J.R.R. Tolkien notes that Ambaróna is the "ancient name of a region", and means "uprising, sunrise, orient"; it is composed of the Quenya words amba "up(wards)" and róna "east".