The director of the Signal Intelligence Service (the army's cryptography division) during World War II was renowned cryptologist William Friedman. He had dubbed his staff at the SIS 'Magicians' and through this the term Magic became used to describe the Japanese messages they had decrypted.
The military establishment picked up on this terminology and it became the codename for all US cryptographically produced intelligence. Hence a Magic security clearance indicated that the individual had clearance to read the cryptographically produced intelligence.
The British equivalent was codenamed Ultra.