think of the king as a person who cares for the people and gives them supplies and they are kinda like presidents. so they are for many things like without the king there would be no queen and even the pawns would run out of supplies The above is a cute answer and I hate to ruin it with the plain facts, but since you asked, the king serves as the target for each opponent to attack and trap and win the game. Each side of the board is an army and the king is the leader so, although he is pretty weak with all the other pieces on the board, when the king is cornered properly, the game is over.
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Unlike the other chess pieces , the king does not have a numerical value assigned to it since the king is invaluable due to it's importance to the game ; the king is invaluable because it's capture is the goal of the game .
One, no king, game over. All the other pieces, while more powerful in their ability to capture other pieces are speifically charged with the tasks of protecting their king and, at the same time, capturing the king on the other side.
The king is important in chess because it's the peice that determines who wins the game. You can achieve victory only be checkmating the king.
The king represents the piece that you want to protect. The object of the game is to checkmate the opponent's king.