An ESN is an electronic serial number. This number is used to identify and verify a cell phone in order to make sure the use of the service is legitimate. The ESN can be found on most devices under the battery cover on an identification label.
The ESN may be used to provide proof of use on an account. Other uses could be for warranty tracking, inventory or time and attendance tracking.
The ESN is useful to track down a stolen device even if the SIM card is changed. It cannot be changed easily and can be electronically checked to prevent fraud.
Your cellular company can identify what type of phone you are using. Most cellular companies require a data package subscription on some phones. They may automatically add a package if you switch to a phone for which one is required.