The Invisible Pink Unicorn (IPU) is the goddess of a parody religion used to satirize theistic beliefs, taking the form of a unicorn that is paradoxically both invisible and pink. She is a rhetorical illustration used by atheists and other religious skeptics as a contemporary version of Russell's teapot, sometimes mentioned in conjunction with the Flying Spaghetti Monster.
The IPU is used to argue that supernatural beliefs are arbitrary by, for example, replacing the word God in any theistic statement with Invisible Pink Unicorn. The mutually exclusive attributes of pinkness and invisibility, coupled with the inability to disprove the IPU's existence, satirize properties that some theists attribute to a theistic deity.
Invisible Pink Unicorns are beings of great spiritual power. We know this because they are capable of being invisible and pink at the same time. Like all religions, the Faith of the Invisible Pink Unicorns is based upon both logic and faith. We have faith that they are pink; we logically know that they are invisible because we can't see them. — Steve Eley
It is common when discussing the Invisible Pink Unicorn to point out that because she is invisible, no one can prove that she does not exist (or indeed that she is not pink). This is a parody of similar theistic claims about God—that God, as creator of the universe, is not subject to its laws and thus not physically detecting him tells us nothing about his existence or lack thereof. The Invisible Pink Unicorn is an illustration which attempts to demonstrate the absurdity of citing attributes and a lack of evidence as proof of a deity's existence. Her two defining attributes, invisibility and color (pink), are inconsistent and contradictory; this is part of the satire. The paradox of something being invisible yet having visible characteristics (e.g., color) is reflected in some East Asian cultures, wherein an "invisible red string" is said to connect people who have a shared or linked destiny.
There are humorous mock debates amongst her "followers" concerning her other attributes, such as whether she is completely invisible, or invisible to most, but visible to those who have faith in her (bearing similarities to "The Emperor's New Clothes"). Some arguments are quite elaborate and tortuous, satirizing the disputatiousness and intricacy of the theological debates that occur in many religions.
Source: Wikipedia, "Invisible Pink Unicorn", available under the CC-BY-SA License.