After you have chosen your delegate, the next step is to grant that person permissions for your calendar. Logically enough, the permissions you choose will depend on how much you want the delegate to do for you.
Your delegate can do most with this feature if you grant the delegate Editor permission. An editor can send meeting requests on your behalf. Also — and this is important — an editor can modify or delete any item in your calendar (including items that the editor did not create). Having these permissions will allow your delegate to perform tasks such as rescheduling an existing meeting (even if the delegate didn't schedule that meeting in the first place).