Adjustment of Status (AOS) is the process by which a non US Citizen petitions the USCIS to become a Permanent Resident of the United States. To qualify the non US Citizen must reside within the United States and meet certain criteria as outlined on the I-485 Form instructions provided by the USCIS. Petitioning for Adjustment of Status can take several months to over a year and will require biometrics to be taken and a formal interview at a local USCIS office. If the person petitioning is the Spouse of a US Citizen then the immigration officer conducting the interview will require proof of a valid marriage as part of their processing.
While a petitioner's Adjustment of Status application is being processed many people also file for (or co-file with their AOS) an Employment Authorization Document and Advance Parole allowing them to work and travel to and from the United States prior to their AOS application process being completed.
[NOTE: The same acronym AOS is used to refer to the I-864 Affidavit of Support form.]