The goal of chess (clearly) is to win the game - to capture your opponent's king. It is a complex and subtle game, and winning the game may involve non-obvious strategies - pulling back at unexpected times, sacrificing pieces and so on.

No human (or, as yet, computer program) is capable of seeing right to the end of the game to play 'perfect moves'. Instead players tend to look ahead some number of moves ahead, and choose the move which they think puts them in a better position. They judge this by the static evaluation function which usually includes things like

• Which pieces are on the board (yours and your opponents).
• How much of the board your pieces can threaten.
• Weather your pieces threaten the center four squares.
• Whether your opponent is is check (ie his king can be captured in the next move)

The static evaluation function is a short term approximation of the utility function. Actual utility is winning the game, but as an approximation, losing pieces is negative utility, capturing opponent's pieces is positive utility, controlling the board is positive utility, and so on.

There is an analogy here with emotion.