Broadus is originally a surname. It became a given name in the South in honor of
John Albert Broadus (1827-1895), a prominent clergyman in the Southern
Baptist denomination.
http://www.sbhla.org/bio_broadus.htm
I cannot find the origin of the surname in the reference books I have in my office, but an educated guess is that it is possibly from the place name Broadwas, a village in western England whose name originally meant "broad tract of alluvial land." (from A.D. Mills's
A Dictionary of English Place-Names>).
A very famous man named after
John Broadus was the founder of the behavioristic school of psychology,
John Broadus Watson. He was born in South
Carolina, like your boyfriend's grandfather.