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Truthiness is a term coined by Stephen Colbert on his Comedy Central fake news show, The Colbert Report.
It refers to a quality that statements can have where they "seem true", or "should be true", or "would (give good story / support my agenda / impress people) if they were true" … without any actual worry over whether they would be judged to be "actually" true by skeptical and disinterested observers.
Stephen uses his gut rather than his head to determine the truthiness of a given statement.
Independently of Colbert's neologism (and possibly predating it), programmers sometimes use "truthy" to refer to data that is somehow akin to a boolean "true" value.