An earned run is any run that scores against a pitcher without the benefit of an error or a passed ball. Often, it is the judgment of the official scorer as to whether a specific run would've scored without the defensive mishap. If a pitcher exits a game with runners on base, any earned runs scored by those runners will count against him.
Many people within the game choose to use earned runs instead of runs when evaluating pitchers because, theoretically at least, the unearned runs a pitcher allows aren't his fault. Earned runs is the key counting statistic used in ERA, the most widely accepted barometer of a pitcher's success.
However, there are a few flaws with using earned runs to judge a pitcher. First, it's a pitcher's job to prevent runs -- not to prevent earned runs. Second, not every error is created equal -- and some plays that are ruled as hits can still be a product of subpar defense.
If there are no errors or passed balls in a given inning or game, all the runs in that inning or game are earned runs.
In A Call
"He allowed X earned"