Irrelevant appeals attempt to sway the listener with information that, though persuasive, is irrelevant to the matter at hand. There are many different types of irrelevant appeal, many different ways of influencing what people think without using evidence. Each is a different type of fallacy of relevance.
Examples
For example, an appeal to authority seeks to persuade by citing what someone else, a perceived authority, thinks on the subject, as if that resolves the question. The degree of support that such an appeal lends to a claim varies depending on the particular authority in question, the relevance of their expertise to the claim, and other factors, but in all cases is limited.
An appeal to consequences seeks to persuade by getting the listener to consider either the attractiveness of a belief, or the unattractiveness of the alternatives. We should form beliefs, however, not on the basis of what we would like to be true, but on the basis of what the evidence supports.
An appeal to pity, which can be very effective, persuades using emotion—specifically, sympathy—rather than reason.
These are just some of the common irrelevant appeals.