When someone or something sounds so farfetched that it is beyond belief.

so unbelievable you have to add fucking for extra umph!
.. my FAVORITE word ..

When something is so hard to imagine, that you just can't fucking believe it.

Something so unbelievable it's incomprehensible or something that is hard to believe.

1. A term to describe something purely awesome and UN-FUCKING-BELIEVABLE!
2. Christopher Walken's hilarious line from the PC game by Take-Two, Ripper.

1) exclamation regarding something that should not have been possible to do.
2) exclamation concerning or referring to something which is impossibly astounding and/or astoundingly impossible.

The only thing in the english language that one can "un" fuck.