If you have moved or plan on moving, you must notify the USCIS. For most people, the easiest way is to submit the change of address online, which will update your address for all pending applications or petitions at the same time. See USCIS’ How to Change Your Address page for more information, including certain situations when you must mail in a paper Form AR-11, Alien’s Change of Address Card.
Unless otherwise noted on USCIS’ page, mailing Form AR-11 alone does not update your address for any pending application or petition. The U.S. Postal Service (USPS) will not forward secure documents such as a permanent resident card (Green Card) or employment authorization document to a new address, so USCIS must receive your new address before it mails these documents to you.
Also, changing your address with USPS will not change your address with USCIS or with the Executive Office for Immigration Review (EOIR) if you have an active or pending court case. Please update your address with both USCIS and USPS (and EOIR if you are in immigration proceedings).