A good clean boost can be used in a couple of ways.
#1) If you have a good tube amp it will increase your signal strength as it hits the tubes, overdriving them and giving you that classic "amp on 11" sound at lower volumes. Only works on tube amps, and only works if you are already running your amp near the verge of breakup. When it does work though, it is magic.
#2) A clean boost is just that, a "clean" volume level boost. It gives you the exact tone you already have just more of it. You would use it like this to raise the volume level of your solos. Great in a setting where you are playing a clean tone (like a good country player with a killer clean tele sound) and you just want it to shine in the mix for a few moments. Gotta have an amp with a lot of headroom to use it this way, otherwise you get the same effect listed in #1.