Since its inception as a crime fighting and investigative unit, the Federal Bureau of Investigation has involved into the largest domestic intelligence gathering organization in the United States. It has the power to track cars and people and monitor cell phone calls without a warrant. Because of its prestige--and its broad powers--FBI background checks are the gold standard in resume verification.
An FBI background check will show all data reported to the federal agency by state and local law enforcement agencies. This will include information regarding any time an individual has been arrested or fingerprinted. Citations and fines may or may not appear depending on whether the local jurisdiction reported these offenses to the federal authorities.
In most cases, an FBI background check is used in conjunction with vetting an individual for a job. Most applications will ask an individual to volunteer information about their criminal records, and an FBI background check can be used to check the veracity of the application responses. An FBI background check can also be part of receiving special privileges, such as those which befall members of a state bar or holders of elected office.
Fingerprints are a major part of an FBI background check. An individual is fingerprinted whenever they're arrested, making it easy to connect concurrent charges with any criminal history. While it's possible for suspicions to be associated with a particular name, it's usually only arrests and convictions that appear on an FBI background check.
An FBI background check provides the service of checking criminal charges in all fifty states of the union. It allows employers or other interested parties from having to file requests in individual states. It doesn't not, however, provide specific information about intelligence gathered about an individual.
Citizens of the U.S. can file a request under the Freedom of Information Act (FOIA) to find FBI documentation concerning themselves or parties to which they may have a verifiable interest. It's through FOIA requests that much of the public knowledge of FBI investigations has been known.