'Earned run' definitions:

Definition of 'earned run'

noun

A run that was not scored as the result of an error by the other team [ant: unearned run]

From: GCIDE

Earn \Earn\ ([~e]rn), v. t. [imp. & p. p. Earned ([~e]rnd); p. pr. & vb. n. Earning.] [AS. earnian; akin to OHG. arn[=o]n to reap, aran harvest, G. ernte, Goth. asans harvest, asneis hireling, AS. esne; cf. Icel. ["o]nn working season, work.]
1. To merit or deserve, as by labor or service; to do that which entitles one to (a reward, whether the reward is received or not). [1913 Webster]
The high repute Which he through hazard huge must earn. --Milton. [1913 Webster]
2. To acquire by labor, service, or performance; to deserve and receive as compensation or wages; as, to earn a good living; to earn honors or laurels. [1913 Webster]
I earn that [what] I eat. --Shak. [1913 Webster]
The bread I have earned by the hazard of my life or the sweat of my brow. --Burke. [1913 Webster]
Earned run (Baseball), a run which is made without the assistance of errors on the opposing side.
Syn: See Obtain. [1913 Webster]