In American colleges, it is the act of being put on academic probation for a second consecutive term, with the possibility of being dismissed if one's GPA is not brought up after the second term. It's called "secret" because the person in question does not want people to know that they are at risk of being dismissed and should be studying instead of doing keg stands.
Originally used in the 1978 American college classic film "Animal House," dean Wormer puts the rowdy Delta Tau Chi fraternity on a "double secret probation," since the Delta House is already on probation. The term has since evolved to mean the act of being on probation while still partying on a regular basis.
Brosef: Let's get those girls from the swimming team over and play some beer pong with them.
Broham: Dude, aren't you on double secret probation?
Brosef: Yeah, whatever. Let's just get drunk with these chicks tonight!