I understand what it takes to earn the Strunk & White badge, but where does the name of the badge come from? What does the name mean or refer to?
William Strunk Jr. & E. B. White were the co-writers of The Elements of Style, a popular American English writing style guide.
http://en.wikipedia.org/wiki/The_Elements_of_Style (via google)
While the other answerers identified the style guide The Elements of Style correctly, Strunk and White were not co-authors, at least in the traditional sense.
William Strunk was a professor of English at Cornell about a hundred years ago, and E.B. White ... took English with him in 1919, purchasing as a required text the first edition, which Strunk had published privately. After Strunk's death, White ... was asked by Macmillan to revise and expand Elements for commercial publication. It took off like a rocket (in 1959) and has sold millions.
Taken from a Chronicle of Higher Education article which goes on to criticize some portions of the book.
Strunk & White are the authors of The Elements of Style, an American English writing style guide.