Daily Activities give you the opportunity to do fun weekly and daily challenges.
When opening the Daily Activity window, you will see the following:

Daily Activities are challenges that you can do everyday. Fill up your daily bar by completing challenges and claim great prizes! These challenges reset DAILY. Tap on the chests displayed above to claim them!

Points that you claim, will also be saved for a weekly challenge. In the same week, you get the opportunity to claim 2 extra chests. You can get an extra chest at 300 points and another one at 600 points. This will reset WEEKLY. Tap these chests in order to claim the contents.

The rewards will be lost if not claimed before the next day/week starts.