Star Collection is an event, during which you can gain extra rewards by collecting stars and unlocking chests.
To get stars you will need to play the Tournament levels. You can get 3 stars for each level.
The rewards from the chests are getting better as you get further in the collection.
NOTE: Usually you will need to get 3 stars on all levels of the Tournaments to be able to unlock the final chest, so make sure you don't miss any levels!