This term comes to us from the Bible (Matt. 3:11), describing a soldier's first experience in battle. Nowadays, it refers to learning something through a difficult means, or overcoming professional or economic hardship to realize success.
This could be experienced at either the individual or institutional level (think: new doctor out of med school gets to work insanely long shifts, or the Volkswagen diesel defeat device scandal, in which they covered up the terrible emissions quality spewed out by their cars through fraudulent engineering.)