A Cadet Challenge is a special type of Away Mission, intended to test your less-experienced Crew members and ensure that they too are prepared to handle the challenges of the ongoing multi-dimensional crisis.
Most Cadet Challenges can only be tackled by Common and Uncommon Crew, with the exception being weekend challenges, in which Rare Crew may participate. In addition, each set of challenges has a particular theme that your Crew must adhere to; you may need to build a Crew of all aliens, all women, or all Starfleet personnel, depending on the scenario.
Cadet Challenges require Cadet Tickets to initiate. All Captains are issued 6 Cadet Tickets per day, with more available to be purchased if you want more rigorous drills for your more fresh-faced recruits. In addition to rewards similar to that of an Away Mission, you will also receive a special reward for completing a Cadet Challenge. This reward, much like the constraints on which Crew can be used, will change depending on the day of the week. You might find a Chroniton boost, extra Training Programs, or a set of Shuttle Boosts.
Like Away Missions, Cadet Challenges have multiple levels of difficulty. The Epic-difficulty missions in particular are designed so that even with the best recruits around at peak performance, it will be challenging and you may not emerge completely successful.
Cadet Challenges can be accessed via the bottom button which cycles between a commendation and Admiral Riker's portrait. They become available at level 10.