It is a topographical surname meaning "brown" or "dark", likely referring to:
* A person who lived near a brown or dark-colored place: This could be a field, a forest, a hill, or even a house.
* A person who had brown hair or eyes: This was a common descriptive term for someone's physical appearance.
The name Braun is quite common in German-speaking countries and is also found in other parts of Europe, particularly those with German historical influence.