Copper is used for spying on other players castles. It is important to send more copper than the castle owner has stocked in the castle you sent your spy to.
If for example the enemy castle has 8000 copper in stock, you have to send at least 8001 copper for a successful spy attempt. In this case your spy will return with a spy report and the enemy won't get a notification.
But if you send only 7999 copper your spy will be captured and the other player looses the 7999 copper. Furthermore he'll get a notification about a captured spy.
At the keep copper can be exchanged for wood, stone and ore. If the keeps level is higher the exchange rate is better.