The costumes that you unlock in the game are not there just to aesthetically improve the appearance of your dragon, they actually offer special powers for your lizard that will help you on your playthrough. All the costumes become available at random, the more common ones can be purchased with coins while the rarer ones with gems. The type of special powers they offer varies and depends on the costume, they include ones that reduce fire, poison, and mine damage.
In total there are 40 different costumes that can be unlocked by leveling up your dragon. To view all the costumes of a specific dragon just select the dragon and tap on the first button in the bottom left corner of the screen. The video below is montage showcasing all 40 dragons and their costumes.