Game means a few different things:

1. An activity with rules that people do for fun or competition. Chess is a game of strategy, tag is a game of speed, and Monopoly is a game of luck and negotiation. Games usually have a goal (like reaching the finish line first or scoring the most points) and rules that everyone agrees to follow. Some games, like soccer or basketball, involve physical activity. Others, like riddles or card games, exercise your mind. What makes something a game rather than just playing around is that structure: there's a way to win, lose, or at least keep score.
2. Wild animals hunted for food or sport. When someone goes hunting for game, they're pursuing animals like deer, ducks, or rabbits. People have hunted game for thousands of years to feed their families. Today, hunting regulations protect animal populations so there will be game for future generations. A game warden is someone whose job involves protecting wildlife and enforcing hunting laws.
3. Someone's approach or strategy, especially in sports or competition. A tennis player might say “I need to improve my game” when working on their skills. When you “up your game,” you're raising your level of performance.

As an adjective, game means willing and eager to try something. The word also appears in many expressions: someone who's game for an adventure is ready to go, and asking “what's your game?” means “what are you really trying to do?”