What does it mean to change your phones ESN?

ESN = Equipment serial number. you can locate this information on the back of the phone under the battery you are looking for a number that starts with a zero or a alpha numeric that starts with the letter A and is followed by zeros and numbers and letters. What you want to do is take that information and log in to your account at verizon wireless.com/myaccount or by calling 1-800-922-0204 from another phone and they will walk you though the activation as well as your email set up. because you purchased your device from Ebay you still maybe able to also insure the device however you would need to contact urion directly. hope this helps.