In English it literally means the carrying out of a required task or action. It is commonly used to refer to administering the death sentence to criminals (the formal term was “executing sentence”), but it has many other uses.
Thus executing a contract can be used in two ways – the act of signing a contract, or the completion by a party of the requirements of the contract. Typically one executes a contract-of-sale when the parties sign the contract; one executes an executory contract by completing the tasks set forth in the contract. A court order is executed by a third party when it fulfils the requirement of the order.