Hand-waving is a pejorative label for attempting to be seen as effective – in word, reasoning, or deed – while actually doing nothing effective or substantial. It is often applied to debating techniques that involve fallacies, misdirection and the glossing over of details. It is also used academically to indicate unproven claims and skipped steps in proofs (sometimes intentionally, as in lectures and instructional materials), with some specific meanings in particular fields, including literary criticism, speculative fiction, mathematics, logic, science and engineering.

The term can additionally be used in work situations, when attempts are made to display productivity or assure accountability without actually resulting in them. The term can also be used as a self-admission of, and suggestion to defer discussion about, an allegedly unimportant weakness in one's own argument's evidence, to forestall an opponent dwelling on it. In debate competition, certain cases of this form of hand-waving may be explicitly permitted.

Hand-waving is an idiomatic metaphor, derived in part from the use of excessive gesticulation, perceived as unproductive, distracting or nervous, in communication or other effort.^{[citation needed]} The term also evokes the sleight-of-hand distraction techniques of stage magic, and suggests that the speaker or writer seems to believe that if they, figuratively speaking, simply wave their hands, no one will notice or speak up about the holes in the reasoning. This implication of misleading intent has been reinforced by the pop-culture influence of the Star Wars franchise, in which mystically powerful hand-waving is fictionally used for mind control, and some uses of the term in public discourse are explicit Star Wars references.

Actual hand-waving motions may be used either by a speaker to indicate a desire to avoid going into details, or by critics to indicate that they believe the proponent of an argument is engaging in a verbal hand-wave inappropriately.

The spelling of the compound varies (both with regard to this idiom and the everyday human communication gesture of waving). While hand-waving is the most common spelling of the unitary present participle and gerund in this usage, and hand-wave of the simple present verb, hand wave dominates as the noun-phrase form. Handwaving and handwave may be preferred in some circles, and are well attested. "Hand waving" is mostly used otherwise, e.g. "she had one hand waving, the other on the rail", but is found in some dictionaries in this form. A more arch, mock-antiquarian construction is waving of [the] hands. Superlative constructions such as "vigorous hand-waving", "waved their hand[s] furiously", "lots of waving of hands", etc., are used to imply that the hand-waver lacks confidence in the information being conveyed, cannot convincingly express or defend the core of the argument being advanced. The descriptive epithet hand-waver has been applied to those engaging in hand-waving, but is not common. The opposite of hand-waving is sometimes called nose-following in mathematics .

However it is spelled, the expression is also used in the original literal meaning of gesturing in a greeting, departing, excited, or attention-seeking manner by waving the hands, as in "friendly were the hand-waving crowds ..." (— Sinclair Lewis), which dates to the mid-17th century as a hyphenated verb and the early 19th century United States as a fully compounded verb. It is unclear when the figurative usage arose. The Oxford Dictionary of English lists it as "extended use", and it appears primarily in modern American dictionaries, some of which label it as "informal".

Handwaving is frequently used in low-quality debate, including political campaigning and commentary, issue-based advocacy, advertising and public relations, tabloid journalism, opinion pieces, Internet memes, and informal discussion and writing. If the opponent in a debate or a commentator on an argument alleges hand-waving, it suggests that the proponent of the argument, position or message has engaged in one or more fallacies of logic, usually informal, and/or glossed over non-trivial details, and is attempting to wave away challenges and deflect questions, as if swatting at flies. The distraction inherent in the sense of the term has become a key part of the meaning. The fallacies in question vary, but often include one of the many variants of argument to emotion, and in political discourse frequently involve unjustified assignment or transference of blame. Hand-waving is not itself a fallacy; the proponent's argument may incidentally be correct despite their failure to properly support it. A tertiary meaning refers to use of poorly-reasoned arguments specifically to impress or to persuade.

The New Hacker's Dictionary (a.k.a. The Jargon File) observes: