This refers to an opinion or statement that contains an abnormally large amount of ignorance. It does not necessarily have to be about the Ohio State University, but the term contracted its title from the majority of Ohio State fans who are disgustingly ignorant about their team, band, fans, etc. being the best in the world, and requiring that everyone who beats them, especially twice in two NCAA championship games, be hated.
Jon: The Cleveland Cavaliers would be much better without Lebron James.
Donald: That is Ohio State ignorance.