At McDonalds, it refers to the notion of a meal that "includes everything." (Except, perhaps, some extra dessert.)
At a resort, the equivalent would be the "all inclusive," where meals and drinks are included in the fee, but where hookers probably aren't.
At a MP, there is the notion of a "Happy Meal" being the one having a goodly set of "extras." With the bad pun of perhaps "munching on a nice fur burger." Much as with the other examples, it probably doesn't involve "full service" (e.g. - penis going inside her), but is probably as much fun as you can get without shopping for particular extras.