There are a number of special items and features that be unlocked by completing Pokemon Contests to certain degrees, as below.

Unlockable	How to Unlock
Contest Star Ribbon & Battle Animation	Beating all five Master Rank Contests with the same Pokemon gives them this ribbon and a special animation when entering battles.
Cosplay Pikachu (gift Pokemon)	Participate in a single Contest.
Glass Ornament Decoration	Win all Master Rank Contests three times each, then speak with the Lilycove museum curator.
Lucarionite & Star Light Decoration	Win all five Master Rank Contests, and then beat Lisia in one.