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.
Caught stealing percentage -- provided the sample size is large enough -- is generally the best way to evaluate a catcher's effectiveness at throwing out runners. It's obviously not perfect, because certain pitchers do a better job of holding runners on than others. But there aren't many better ways to assess how well a catcher did his job at shutting down opposing running games.
The main flaw in using this metric is that certain catchers -- those whose great arms carry reputations -- are run on less frequently, and often only in situations conducive to the runner.
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"