In the Soviet Union (and briefly in the Russian Federation and other Warsaw Pact countries): a permit entitling a person to reside (and therefore work) in a particular city or town.
The propiska system was introduced in 1932 as an attempt to control population movement from the countryside to the towns. A propiska not only controlled a person's residence and workplace, but also access to benefits, etc.
1950s. From Russian propiska registration, residence permit from propis-, stem of propisat′ to register + -ka, suffix forming nouns.