Every track in the main Career (Qualify) mode has 3 Track Challenges. These Track Challenges are optional challenges you can complete for extra silver coins and rep. In order for the challenge to count you must place in the top 3.
You can see a list of the track challenge in the top left of the screen at the start of a race. Once the race starts the challenges will collapse automatically. If you start to complete a challenge the challenge with expand again. You can also see the challenge by hitting the pause button, or by hitting the info button from the track selection screen.