The term is derived from the saying stores use to let people know they are always available 'Open 24/7.' In the same way 24 7 69 lets people know you are always available for some hardcore 69ing if you are not already doing the sensual act.
Andrew: Oh! Its because he follows the lifestyle known as 24 7 69!
Wilson: What's that?
Andrew: Why don't you open his door and find out?
(door is opened upon Andrew's roommate Ignatio 69ing with an obese woman wearing a paper bag with a picture of Wilson's face on it)
Wilson: Oh GAWD!!!!! (cries out of pure trauma)