They reduce pressure put back on the turbo when you let out of the throttle. Its basically a vent and will stop the compressor wheel/shaft from stalling and still spin freely. It also allows for better spool up again when you get back on the throttle.
I think losing HP would only come from if the BOV is leaking and your not able to gain full boost.
Be careful what you buy. I had 2 TurboXS RFL's and they BOTH leaked, out of the box. I would do some research first and go for performance and not so much sound. FWIW, I will going with the Synapse.