Adjustment of Status (AOS) refers to the process by which a foreign-born person who is in the United States can change immigration status to that of a lawful resident (or green card holder) after meeting certain eligibility requirements; and get all the way to approval without having to leave the United States.
This process is, for most types of cases, provided for by § 245(a) of the Immigration and Nationality Act (8 U.S.C. § 1255). The main benefit of this process is that it allows applicants to deal entirely with U.S. Citizenship and Immigration Services, rather than traveling to an overseas U.S. consulate for the final step in gaining approval for U.S. residence.
Obviously, the first AOS requirement is that the applicant meets the basic eligibility requirements for a green card; and if they're applying in a "preference category," which is subject to annual limits, that an immigrant visa number is actually available by the time of requesting AOS. (Another way of saying this is that the person's "priority date" has become current.) Many, but not all family- and employment-based visas are subject to these annual limits; and because demand usually exceeds supply, waiting lists have become a standard part of the process.
Another hurdle that all applicants must overcome is showing that they are not "inadmissible" to the United States, for example because of a criminal record.
However, there are certain people who, though perhaps otherwise eligible for a green card, are NOT eligible to obtain it by the process of adjusting status within the United States. The main ones are:
Consult an attorney about the various exceptions that might apply to you. For example, asylees and refugees can apply for adjustment under a separate section of the law, I.N.A. § 209(b) or 8 U.S.C. § 1159(b). U visa holders can adjust under I.N.A. § 245(m), 8 U.S.C. § 1255(m). Self-petitioners under VAWA are exempt from all of the adjustment bars.
And don't forget, adjustment of status is not the only procedural option for obtaining a U.S. green card. It might still be possible for you to obtain a green card via the alternate procedure, "consular processing."
Someone who meets the various requirements described above and is not subject to any ground of inadmissibility might be able to adjust status to that of U.S. lawful permanent resident. The procedure for doing so is by submitting to USCIS a Form I-485 (Application to Register Permanent Residence or Adjust Status) with all other mandatory forms, relevant documentation, and current processing fees. These must be sent to the USCIS service center for the applicant's region. (In-person delivery is impossible.)
It is particularly important (unless you fall into an exception, such as for asylees or VAWA applicants) that you include proof that you were inspected and lawfully admitted to the United States as part of your adjustment packet. Most likely you would do this by submitting a copy of your Form I-94 Arrival/Departure Record (which in some cases is given to entrants by CBP (Customs and Border Protection) on paper, but which you'll more likely find in its online database).
After USCIS has received and accepted your AOS packet, it will schedule you for a biometrics appointment where your fingerprints and other information will be gathered; and later a personal interview at a USCIS office in your region.
The applicant must, by law, remain physically present in the United State in order to apply for AOS. Exiting the country during the application process could be considered as abandonment of the adjustment application. Nevertheless, this is easily prevented in most cases by applying for prior permission ("advance parole") along with your AOS filing or even afterward. It requires submitting Form I-131 and paying an additional fee.
Some nonimmigrants with temporary work visas are, however, exempt from filing an application for advance parole.
If you have any doubts about any aspect of your eligibility or procedures with filing an AOS application, or if you're daunted by the mountain of paperwork that's involved, consult an experienced U.S. immigration attorney. The attorney can assist you in all aspects of the AOS process and accompany you to the USCIS interview.