Radius refers to the curvature of the neck. stewmac.com has some templates that you can use to determine what yours is, I'm sure the local guitar shop will have them as well. I'd be hardpressed to believe that the radius will affect how a guitar sounds, but definitely will affect the playability.
Check this out: http://www.warmoth.com/Guitar/Necks/compound.htm
when you look down a guitar neck(looking from the back of the body at the head) the arch left to right is the radius, yes, the radius can affect tone, because some radiuses buzz when you bend the strings.
Generally speaking the smaller radius fingerboards make chording easier because they conform to the "natural" curvature of the fingers. The downside is that you can
"fret out" (hit another fret) when doing large bends. Larger radius fingerboards are better for soloing and bends.
If you buy the book "How To Make Your Electric Guitar Play Great!" by Dan Erlewine (and you should) it includes plastic radius gauges.