It's like saying, "Fuck Me", but usually referring to a fucked up situation and not yourself, even if you screwed up.
Trying to open a jar of peppers. You banged the lid with the back of a knife, ran it under hot water and yet nothing gets it open. Out of anger and wanting to throw the jar across the room, one exclaims, "Mother Ass F, this is one fucking hard jar to open!"
Taken from "Bloody Hell", (see in this dictionary), this phrase emphasizes a double fuck without actually using the word once and therefore, appropriate to say in public.
So in that sense, it's like saying, "What the fuck?" but twice, "What the bloody F?!"
Wife: Some asshole actually wrote with shaving cream on our car.
Husband: What the bloody f?! I just had it washed.
Wife: What the bloody Q, What the bloody P... (pick a letter).