This song about marijuana originally showed up in a "Monstervision" video, The Adventures of Mary Jane Holland, which Gaga posted to YouTube on August 19, 2013.
The usage of Mary Jane as a slang term for marijuana is an obvious one given their similarities. The word marijuana itself derives from the Mexican Spanish word for the drug, marihuana. Other Pop artists who have used the phrase as a song title in a weed context include Tom Petty and the Heartbreakers, Rick James and probably The Association.
Gaga explained during a Sirius XM special that Mary Jane Holland was an alter ego she adopted while smoking weed in Amsterdam to help with her anxiety.