"Way out" in this context simply means "a long way away". It is actually a contraction of "a long way out of here". The "boonies" are, roughly speaking, the "distant places". fdmaxey is correct that it refers to an unpleasant rural place where there is nothing fun happening. So the whole idiom conveys the following "he lives a long way away, in the boring, distant, rural places."

"Boonies" = "boondocks" The boondocks is an unpleasant out-of-the-way rural place. It is uninteresting and sparsely populated.

The explanations given above me are spot on, you could see for further reference the movie "The Boondock Saints" and the song, "Where is my mind" by The Pixies. Lyrics... (where is my mind?, way out, in the water, see it swimming.) good luck with your English learning Николай!