The "Tinkerbell fallacy" refers to the practice of considering a fictional entity's reaction to our possible disbelief in them.
In the book "Peter Pan", at one point Tinkerbell the fairy is near death, but "she [thinks] she could get well again if children believe... in fairies". Clearly, the reader or listener is being encouraged to affirm their belief. This is made explicit in stage productions, where Peter Pan exhorts the audience to clap. Of course, Tinkerbell is only real in the fictional world of the book or play, not in the real world of the audience. Yet by suspending their disbelief, the audience has granted this fictional idea the status of a person. Some people feel that it is virtuous to clap, because not clapping would feel like betrayal, even though the person being betrayed is not real.
Obviously, "Peter Pan" is intended for children, and some adults only clap to go along with the children. But the same fallacy is embraced by many adults, and is a major support for belief in a god. Although a god, unlike Tinkerbell, is typically portrayed as angry, vengeful, or sad, rather than hurt, by our disbelief, the effect is the same. Once we've thought of a god as being a real person who knows our thoughts, it is difficult not to imagine that person's reaction to our disbelieving thoughts, even though that's illogical.
In other words, the Tinkerbell fallacy is an unjustified generalization from the fact that trust in one's friends is often a virtue, to the superficially similar idea that faith in one's god is also a virtue. We grant our friends the benefit of the doubt; an unproven abstraction does not deserve the same treatment. Once one believes that faith is a virtue, that motivates one to construct elaborate rationalizations to justify that faith.
The phrase "Tinkerbell fallacy" is also sometimes used to refer to mistakenly thinking that our inner beliefs affects nonfictional events, and thus that a good result will happen if we just believe hard enough. However, this is not necessarily a fallacy at all, as, through our actions, our beliefs can indeed affect reality.