Historically speaking, one of a handful of major industrial magnates from the late 19th and early 20th centuries, such as Andrew Carnegie, John D. Rockefeller, John Jacob Astor, Cornelius Vanderbilt (among others). Renowned for their wealth, they were also renowned for sometimes unscrupulous business practices.
In modern times, this term generally refers to that wing of the Republican Party that supports the welfare of rich people to a sometimes ridiculous extent. Robber barons generally support lower taxes, decreased regulation of businesses, and privatization of government. The robber baron wing often overlaps with the glibertarians in economic matters. Robber barons, in general, care about social issues only to the extent that the talibangelicals force them to.
When Senator Booger voted against tax cuts for the wealthy, a chorus of robber barons gathered to create a storm of poutrage against him.