Caught stealing percentage refers to the frequency with which a catcher throws out opposing baserunners who are trying to steal. The formula is simple: catcher caught stealings divided by total stolen-base attempts -- both successful and unsuccessful -- against that catcher.
In terms of caught stealing percentage, a catcher is not responsible for any runners who advance via a passed ball or wild pitch. (A catcher also does not receive credit for throwing out a runner who tries to advance on a passed ball or wild pitch.)
"he's thrown out X percent of potential base-stealers," the opposite: "stolen-base percentage against"