Argument from incredulity is a fallacy where one treats their own incredulity as evidence for or against a proposition. Incredulity is of course the opposite of credulity which refers to a willingness to believe with insufficient evidence or proof. That definition of credulity would make it a near synonym for gullibility which would seem to indicate that incredulity is a good thing. In practice it amounts to doubt or skepticism which are good when applied to false things and bad when applied to true ones. As far as arguments go this amounts to passing out checks and acting like they are cash. Coming from an expert incredulity is a credible signal that we shouldn't believe a claim and one can adjust their credence according to the speaker. Regardless of who is talking this isn't an argument. The typical format for an argument from incredulity to take is expressing that something is unbelievable, express derision at anyone who disagrees, and emphasize how obvious the position is and how stupid people are for not seeing that. Repetitiousness is important since anybody who disagrees must be really dumb.
Argument from incredulity replaced argument from consequences as my top choice for most infuriating fallacy. It's not that it's wrong. All fallacies are wrong. It's that it's a vacuous time waster. There is an implicit assumption when one is trying to argue about something in the outside world that they will at some point make claims that aren't about their personal feelings. Other fallacies tend to happen quickly but an argument from incredulity is a waiting game where the listener is continually hoping the speaker will launch into an explanation of why they feel that way. It could happen. It could begin the very next sentence or the one after that.
Argument from incredulity is subtly different from argument from ignorance. Ignorance requires that the speaker not understand the other position while incredulity simply requires that they find it impossible to swallow. Many (perhaps most) arguments from incredulity have some basis in ignorance and one would hope that knowing more might prompt valid reasons for disagreement. It's important to remember that it is normal for a person to express incredulity in an argument and even if they commit this fallacy it isn't proof that they are wrong; merely that they are using invalid argumentation.