A Social Security number (SSN) in the United States is a nine-digit number issued to U.S. citizens. Permanent residents and temporary (working) residents under section 205(c)(2) of the Social Security Act. The Social Security Administrator is responsible for issuing SSNs. Social Security numbers are ostensibly used for Social Security purposes, but in the US they are used almost as an ID number for taxation and other purposes.
A social security number is necessary to work in the United States. But having a social security number is not the same thing as having a work authorization. Immigrants can choose to apply for SSNs as part of their adjustment of status application or file the application at SSN office after they become permanent residents.