A contest can represent a desire to win something genuine and meaningful. However, it can also carry the connotation of a fight, struggle or rivalry to be the best by bringing forth your disciplined work and passion for creative arts.
Dreaming about winning a contest is an indication of what you want in your life and how you perceive of it. It keeps your head in the game, never wavering to the outside noise of partying and entertainment, while you continue to work on your craft with the end goal in mind.