The invisible pink unicorn is a mind-tool used by skeptics. It is a practical application of Occam's razor.
for instance, when faced with a crank giving you his latest theory on UFO abductions, Atlantis, telepathy or suchlike, you may say that you think his theory is rubbish.
"But", they will argue, "you have no evidence against it. You don't know for sure that it's rubbish". This is true. However there are an infinite number of bizarre theories that you don't have any proof against. For instance, how do you know that there isn't a Bengal tiger under your bed right now? If you look and find no tiger, it must have teleported out. Aha! a teleporting tiger! You have no proof that its not so, so you can believe it!
How do you know that there isn't a space alien in your bathroom, using your toothbrush as an anal probe? Or that the President isn't really a space lizard. I could make up stuff like this all day, and some of it is even plausible. When I said infinite I really meant it.
The most well known example is this: how do you know that there isn't an invisible pink unicorn nearby. You wouldn't even see it, it's invisible. Yet you know instictively that it's not true. Why? Because you somehow know that I made it up just to annoy you. And besides, if it is transparent, how can it be pink?
So when someone picks a particular theory to believe, they could be believing from one of two reasons: evidence or wishful thinking. If there is more of the latter than the former, you are right to dismiss their theory as just one more nonsense.
At some level, people have a instinctive grasp on Occam's Razor. Yet at another level, it is a difficult principle to keep in mind. The invisible pink unicorn is a mind-tool to help remind us.
It is a reply to the truth that absence of proof is not proof of absence with another truth: extraordinary claims demand extraordinary proof.
Carl Sagan use a variation of this argument, with an invisible Dragon in The Dragon In My Garage