To have a really good time. The reference is to late dwarf actor Billy Barty, the 3'9" man who, despite his diminutive stature, was renowned for his long showbiz career and effervescent character.
Often when someone spills or breaks or drops something at a party (often resulting in a mess or general spectacle), or when someone does something embarassing or dumb.
Usually accompanied by someone actually yelling, "Party Foul!" while everyone else laughs because they're drunk.
** Jake drops beer and spills it all over the floor.