Hepburn is a family name of the Anglo-Scottish border, that is associated with a variety of notable people, eponyms, places, and things.
Alternatively it could mean something along the lines of "high place beside the water", as the word burn is a still widely used in Northumbrian and Scots for stream.
This was the seat of a line of the family until the eighteenth century when that branch died out, having left only a female heir.
This branch of the family originated in Lothian when a Hepburn was granted land having saved the Earl of March from a horse that had lost control.
All of these families were prominent in various ways at various junctures of Scottish history, but all were primarily located around the East Lothian area.