defeat
To win against someone so they lose.
To defeat someone means to win against them in a contest, game, battle, or competition. When your soccer team defeats the rival school, you've outscored them and won the game. When a chess player defeats an opponent, they've outmaneuvered them to checkmate their king.
Defeat works both ways: as a verb meaning to beat someone, or as a noun describing the loss itself. A general might defeat an enemy army in battle, while the losing side suffers defeat. When your favorite team experiences defeat, they've lost the game, even though they tried their best.
The word carries a sense of finality: someone set out to accomplish something and couldn't do it. You might defeat a difficult level in a video game after many attempts, or feel defeated by a challenging math problem that you just can't solve. When people talk about admitting defeat, they mean accepting that they can't win or succeed at something, at least not this time.
Defeat doesn't mean the end of everything. Many inventors, athletes, and leaders have experienced defeat before eventually succeeding. Abraham Lincoln lost several elections before becoming president. Thomas Edison tried many times before inventing a working light bulb. Defeat can show what doesn't work, so people can try a different approach next time.