The S, R and 22 actually do not stand for anything, thus are not short for any words. Some have thought they were for State Requirement - form #22.
The SR-22 is just the title of the form that states and insurance companies use for when financial responsibility must be filed with the state. Some states may refer to it as the certificate of financial responsibility or the FR form as well.
We verified the meaning of the SR22 with the Florida Department of Financial Services, which serves as the regulating authority over the banking and insurance industry in Florida as well as the FL Department of Highway Safety & Motor Vehicles, who has jurisdiction in Florida over the SR-22.
Both state agencies confirmed that SR-22 is simply the name of the form used by the insurance company stating that auto liability insurance is in effect for a particular individual.
Follow this link for an auto insurance quote for Florida or another state which requires the SR-22 for certain individuals.