This refers to the January 19, 2010 US Senate election in Massachusetts to fill the seat vacated by the late Ted Kennedy. Republican Scott Brown convincingly defeated Democrat Martha Coakley, who was overwhelmingly favored to win in a state that had not elected a Republican in 40 years.
The term is distinct from "brown noise". In science, Brownian noise, also known as "Brown noise" or "red noise", is the kind of signal noise produced by Brownian motion. An example of Brownian noise is the sound a television speaker makes when the screen goes to static.