Unless revoked, travel authorizations are valid for two years from the date of authorization, or until your passport expires, whichever date comes first*. The Authorization Approved screen displays your travel authorization expiration date.
This means that as long as you received an ESTA authorization to travel, you do not have to reapply during the validity period.
If your ESTA expires while in the U.S. it will not affect your departure.
Note: Is it important to PRINT a copy of the document for your records. The printout is not required upon arrival into the United States, as the officers have the information electronically.
Receiving ESTA authorization does not mean you may stay in the U.S. for two years. It only allows you to travel to the U.S. under the terms of the Visa Waiver Program (VWP), which only allows you to stay in the U.S. for 90 days or less. If you plan to stay for longer than 90 days, you must obtain a visa at the nearest U.S. Embassy or Consulate.
*If you obtain a new passport or change your name, gender or country of citizenship, you will be required to apply for a new travel authorization. This is also required if one of your answers to any of the VWP eligibility questions changes.