This is one of my favourite techniques within music (if it even is one). As such I would love to know what its called, thanks :)
If you're a musician, "tacet" ("silent") or "rest". If you're the vocalist, "a cappella" ("in the manner of the chapel").
If you're a sound engineer looking at a soundboard, you "solo" the channel (after the name of the button on the vocalist's channel on the board). This is very rare unless you're doing live looping and are doing your own sound.