The story
On a ship, “colors” means its flags. By the late 1500s, English sailors were already using the word that way. A ship’s colors told everyone at sea who she belonged to.
In a sea battle, a ship that gave up lowered its flags. Sailors called this striking her colors. A ship that held her own kept her colors flying, and could sail home with every flag still high.
That picture of proud, flags-up success moved ashore. By the 1700s, people who came through a hard trial in good shape were said to come off with flying colors.
The verb changed over time. “Came off with flying colors” was common for many years. Later, school exams made “pass” the favorite, and passing with flying colors is now the usual way to say it.
