The tickets can be used to play Challenge and Mayhem levels.
 
To play a Challenge level using a ticket:
Go into the ‘Tribes’ screen and select one of the characters from the current season. Then click on the Challenge button at the bottom of the screen. Complete 4 challenge levels to open a chest and earn rewards.
 
To play a Mayhem level using a ticket:
Go into the ‘tribes’ screen and select one of the characters from a previous season. Then click on the Mayhem button at the bottom. Complete Mayhem levels to get an XP boost and earn rewards.