Trainer Card
Nintendo introduced Pokemon Trainer cards in the Pokemon Emerald generation of games. The trainer card lists all of the achievements of the player and can be shown online for bragging right. The color of your trainer card reflects the rank you have as a Pokemon trainer. The colors, in order of lowest to highest, are green, bronze, copper, silver and gold. Completing the Pokedex will change your card to the next highest level.
Additional Star
Stars reflect the level you have achieved as a Pokemon trainer. Average trainers never achieve even one, but as you're aiming to become the best there ever was, your goal is to get all four. You receive a star for getting a record in the hall of fame, getting a master rank in all of the Pokemon contests, getting gold medals in the Battle Frontier and completing the Pokedex.
NCP Reactions
Depending on your trainer rank, which is determined by your card color and stars, different non-player characters will react to you in a different fashion. For instance, the Pokemon Center Nurse who heals your Pokemon will treat you with more respect the higher rank you achieve. Completing the Pokedex will bump you up a rank, causing the next level of NCP reactions to activate.
Bragging Rights
The Pokemon franchise has an intense, hardcore group of enthusiasts who, since Pokemon Emerald, can interact online through their gaming devices. Whenever these players interact, the website displays their trainer cards. Players of older games in the franchise who have not completed the Pokedex are not taken as seriously. Players of newer games can still see your trainer card from previous games and your rank carries over to newer games when you link them, allowing you to display how long you have followed the franchise.