The Challenge system is based on daily quests, most often associated with a Dungeon or Raid instance with their respective Daily Quest. These reset and change every day at 4AM Server Time. Completing said Challenge can reward you with such treasures such as XP, upgrade materials, and a special currency called Solar Energy to purchase rewards from the Dragon Express.
By completing a specific set of tasks, you will then be able to open your Daily Challenge window and claim a set of rewards. Each day at 6 AM server time, the tasks will reset. If you miss to complete the Daily Challenge, you will instead stack Rest Rewards. Rest benefits can stack for up to 2 days and can be claimed by completing a Daily Challenge.
Weekly Challenge works in the same way, but is mainly finished by doing Raids and provides higher rewards than the Daily Challenge. As you might have guessed on its name, the Weekly Challenge can be done once every week and resets on Wednesday at 6AM Server Time.