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From urban dictionary:

Also written handwaving. In formal conversation / speech omitting important details about the subject matter either because 1) the audience is perceived to be ignorant 2) the speaker themselves is not well-informed on the subject matter or 3) a little from column A and a little from column B.

I can understand that definition, but I wonder, why does "Hand Waving" have a meaning "omitting important details"? Is there a story behind that?

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It mainly seems to be a reference to the literal physical act of waving your hand when telling someone not to worry about the details of something. I'm not sure if the gesture is international in use, so it looks very similar to the gesture made to shoo a bug away from your food.

Hand waving is used quite often in fantasy novels. The term "hand waving" is used if the author explains something "because magic." In other words they are saying - don't think too hard about it, just go with the premise I have set up.

An example would be the way many things work in the Harry Potter universe. Many things don't follow basic laws of phyics because Rowling has "hand waved" the physics by saying it's that way because people can use magic.

A more realistic example of hand waving would be a person omitting very technical or unnecessary details when giving someone information. I.E. A doctor tells a patient they have cancer. The patient asks how the doctor knows this. The doctor replies they did a biopsy. The doctor is "hand waving" many details about the exact chemical process used in the blood test. But the patient doesn't need to know those details, and probably wouldn't understand anyways.

The opposite of our doctor example also occurs quite often. The first example that comes to mind being on the playground! An excellent example of a presenter "hand waving" details would be: Child A claims X. Child B asks how A can know that. Child A replies "That's what my Dad says!" Child A has "hand waved" many details because he does not really understand what he is trying to explain.

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I think the problem is you're using the "Urban Dictionary".

Handwaving would not be used to omit important details, but to omit trivial details. This is especially true from the context of the rest of the definition.

In fact, I would say the entire definition is poorly-worded. Typically, handwaving is used to omit trivial details about the subject matter, because the audience is already aware of the details and does not need them explained.

If the audience is perceived to be ignorant, why would you leave out important details? If the speaker is not well-informed on the subject, how would the speaker know which details are important or trivial to begin with, and at which point it might be appropriate to waive away details?

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