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Background checks are performed by a variety of agencies' databases. A national background check will be made by the FBI, which you yourself can make by calling their office in Fredericksburg, VA (or is it Harrisburg, PA? my sick mind forgot..). FBI's information will also encompass any information in the NCIC (National Crime Information Center).
Background checks will also be made on the local state Bureau of Investigation's databases. This, say, if you are in Georgia, will be Georgia Bureau of Investigation's (GBI) databases. This will include the state CIC's databases as well (for ex: Georgia Crime Information Center).
For all these background checks a NO RECORD FOUND result is desired. If a RECORD FOUND is obtained, that is undesirable and under most circumstances will warrant a transfer to local district office for interview/processing.