There are a number of things to earn from Pokémon Contests.
Finish a single Pokémon Contest and you can receive a Cosplay Pikachu ! This unique Pikachu can don one of five types of costumes during contests and battles (and minigames, etc.), with each costume providing a specific signature move.
Whenever you finish a Pokémon Contest, speak with the various people in the entrance area of the Hall, which contain a number of your fans. These people will be able to give you a variety of items, mostly Berries and other minor items.
About the best you’ll get from people are the various items - like Comet Shards and Stardusts - that you can sell for a fair sum of money.
Whenever a Pokémon completes a Master Rank Contest of a certain type, it will be given a Ribbon to document such.
Paintings and Glass Ornament
If you win a Master Rank Contest, you will have a special painting made for you. In the Contest Halls, there’s one painting per Contest type, though you can have three per Contest type in the Lilycove museum (it’s west of the Dept. Store).
If you fill up the museum’s paintings - that is, win three Master Rank Contests in each type - you can speak with the curator to obtain the Glass Ornament decoration for your Secret Base.
Lucarionite and Star Light
For this, you need to beat all five Master Ranks Contests and Lisia will meet with you, telling you that you’ll face her in the next Contest. She’ll be much harder to beat than most of the AI players. If you beat her, you’ll receive the Star Light Base Decoration and the Lucarionite Mega Stone.
Special Pokémon Animation - Contest Star
This can only be done when you finish all of the Master Rank Contests with the same Pokémon. This Pokémon will be given an extra Ribbon - the Contest Star - and will also get a special battle animation in which a shine and faint ribbon appears over it, proving it is a Contest Star!