Congratulations! You won a trophy!
In Crash Team Racing, Crash Nitro Kart, and the Nitro Fueled remake of Crash Team Racing, trophies are obtained by finishing in first place in a trophy race. Collecting all four trophies in each area (three in Nitro Kart) opens up the boss for that area.
After gaining a trophy from one race, another one will open (with the exception of starting with two open when the player first enters an area).
In Crash Bash, trophies are obtained by winning an event three times. Trophies are needed to progress through the game.