Clamp Meter Working Principle
It doesn't specifically measure rms values -- those are calculated from the output of the current transformer portion.

The current clamp is basically a transformer with 1 turn for the primary and 'N' for the secondary. A low value resistor loads the secondary. By transformer theory, I(pri)/I(sec) = N, and V(sec)/V(pri) = N. Also, with the R load, V(sec)/I(sec) = R.

So you get 
I(pri) = N.I(sec) = N.V(sec)/R

So, you just measure the voltage across the secondary resistor; the primary current is this times N/R. Note there is effectively a small resistance placed in series with the primary (by the clamp itself) -- it's basically equal to R/N^2.

Q.E.D.