Trophies are items that appear in every Mario Kart game. They are given as awards for racers that place first, second, and third.
The appearance of the Trophy varies depending on what the player places in the end. The Trophy's design at the top also usually is the same as the cup the player was competing in (if the player was playing the Mushroom Cup, then the top of the Trophy will have a Mushroom on it). If the player places third, then it will be a bronze trophy. If they place in second, the trophy will be silver. And if they place in first, the trophy will be gold.
Although they don't mean much if the player wins them, Gold Trophies actually play a big role when it comes to unlocking other courses and other characters. In games like Mario Kart 64, if the player gets gold Trophies in all of the Cups and CCs, then they will unlock Mirror mode for all of the courses.