The Visitors' homeworld is an unnamed planet where the unnamed Visitor species inhabit.
Anna described the planet as similar to Earth, with vast cities and massive oceans, etc. but they are running out of water and a mineral which is essential for existence. She also states that her people do not divide themselves into countries, implying a single, planetary government.
The cast & crew have stated in several interviews that one of the major points about the Visitors in the new series is a strong anti-environmentalist streak, with the implication being that they strip-mine planets, including their own homeworld, wrecking them in the process, and Earth is next. Given how strongly Anna was trying to emphasize in her TV interview that the Visitor homeworld was a lush paradise comparable to Earth, the scene seems to imply that Anna is lying.