Appeal to popularity (appeal to majority) is the fallacy of claiming that a conclusion is true or credible because most people believe it.
The form of the argument is generally:
1) Most people believe X
2) Therefore X is true
Another version of the argument is the reverse of the above where a lack of acceptance is taken to prove that something must be false. It's form is simply:
1) No one (or almost no one) believes X
2) Therefore X is false
It would be an obviously poor argument to suggest that a claim is true simply because a certain number of people think it's true. Yet it's doubtful that most people who use these sort of arguments are following this line of reasoning. It's more likely they reason (perhaps implicitly) that there would not be popular acceptance of the claim unless there existed other good evidence for thinking it to be true. When thought of in this way, it seems reasonable that an appeal to popularity can be seen as providing some evidence. The problem with this line of thinking is that people often make rash decisions, have limited information, do not search out and fully weigh evidence and fall prey to logical fallacies and cognitive biases. As such, we can say that appeals to popularity are not always irrelevant but is generally considered weak evidence which alone provides insufficient evidence for accepting a claim.
Logical Self-defense, Johnson & Blair
Fallacies: Classical and Contemporary Readings
Argumentum Ad Populum, http://philosophy.lander.edu/logic/popular.html