An Executor (also known as a Personal Representative) makes sure your will is carried out. Your Executor should be someone who is likely to outlive you, and someone you trust with financial matters. You will want to ask them beforehand if they're willing to serve as an Executor. You will also want to designate one or two backups, in case the first Executor is unable to carry out his duties.
If you don't have an Executor, the court will appoint him. But it's standard to name an Executor in a will, and your choice will probably follow your wishes better than someone the court chooses. You might as well name your Executor in your will.