Of Scottish/English (and sometimes Irish) origins, the name is derived from Old English wudu or "wood" (meaning "forest"), and burna or "burn" (meaning 'spring, stream'). They acquired their surname by the area where they lived, "by a stream flowing through the wood". Scribes in the Middle Ages spelled according to sound, resulting in an enormous number of other spelling variations. These include: Wodeburn, Wodburn, Woodburne, Woodbine, Woodbourne, and Whiteburn
The river refered by "burn" may be the River Rede, which runs through the villages of West Woodburn and East Woodburn. However, references to Woodburns span from Edinburgh in the north, to Ayrshire in the west, Dumfries in the south, and Northumberland in the east. There are many rivers that could have been associated as the "burn", and we just don't know.
During the Middle Ages, when migration for the purpose of job-seeking was becoming more common, people often took their former village name as a means of identification, thus resulting in a wide dispersal of the name.
As of 2023, there were somewhere between 2,651 and 3,514 Woodburns living in the United States, 2,214 in England, and 812 in Scotland.