Tickets are used to enter Style Challenges!  Different numbers of tickets may be required for entry depending on the type of challenge.
Your ticket count is shown at the top of the main screen.
Tickets earned by voting are capped at 75, so make sure to use your tickets if you are close to the cap before claiming more! Otherwise, any Tickets that go over the 75 cap will be discarded.

Please note that the Ticket cap of 75 ONLY pertains to earned  tickets, and not to Tickets purchased with Diamonds.