We'll start with the basics.
He teaches economics at Randolph-Macon College in Ashland, Va. Brat, who has a PhD and a Masters of Divinity, teaches mostly introductory economics classes at the college, a small liberal arts school outside Richmond. His faculty Web site (which hasn't been updated recently), features photos of Adam Smith, John Calvin, Friedrich Hayek, and John Maynard Keynes in the four corners. (If you're curious, his students give him moderately decent ratings as a professor.)
Brat was backed by the tea party. In addition to being backed by prominent conservatives (Ann Coulter, Laura Ingraham), Brat was backed by grass-roots tea party groups as well. As the National Journal notes, Cantor's district became more conservative in the most recent redistricting, including adding new areas to his district, making an ideologically-driven challenge more possible.
In May, Cantor addressed the state Republican convention, where he received a negative response from some of the activists in the audience.
Brat is not a "liberal college professor." No doubt hoping that conservative voters would bail on Brat's candidacy, Cantor labeled him a "liberal college professor," which FactCheck determined was inaccurate. The site asked conservative economist Richard Rahn for his assessment of Brat and was told that "he always portrayed himself to me as very conservative."
As if to hammer home the point, Brat's previous research includes a study titled, "An Analysis of the Moral Foundations in Ayn Rand." (Brat says he is not a Randian.) He frequently trumpeted the six elements of the "Republican Creed" on the campaign trail, which you can read on his Web site.
He ran for the Virginia House of Delegates in 2011. In August 2011, Brat announced that he would run for the Republican nomination for a House of Delegates seat. The party chose to run someone else in the general election. (He won.)
Brat was massively outraised. According to his most recent filing with the FEC, Brat raised only about $206,000 through the middle of May. Cantor, on the other hand, raised $5.4 million this cycle.
He will be running against one of his colleagues in November. As we noted earlier on Tuesday, Brat will face Jack Trammell, also an instructor at Randolph-Macon. If the students of the college were to pick, they'd likely pick Trammell; his Rate My Professor score is much higher.