Every day you can take part in a lottery and collect a piece of dust (3 different kinds) or a part of a special item. The purpose of collecting or manufacturing (by using dust) those parts is to build an item which grants you a certain bonus.
For CC you can increase your chances and the number of used items.
For building an item you need at least one piece/part. The rest can be manufactured with dust. If you don't have enough of the needed dust, you can gain it by transforming other parts (of not needed items) or other kinds of dust. Of course this transformation isn't very cost-efficient.
For further details about the specific bonus of an item consult the exhibition room of the museum.