The upper stage gets left behind in Earth orbit. The Briz-M stage provides the kick to propel the payload to a higher orbit and then usually there's a kick motor that follows up, in this case, delivering a Trans-Mars Injection maneuver to set the spacecraft on its way to Mars.

EDIT: Actually realised I'm wrong since the Briz-M is the 4th stage, not the 3rd. The 3rd stage remains in orbit and then splashes down and the 4th stage actually provides the entire kick for TMI [1]

[1] http://blogs.esa.int/rocketscience/2016/03/13/why-exomars-ri...