Provenance is where a thing has been and who has owned it. For some objects it is a footnote. For others it is most of the value.
When it matters most
Signed anything. A signature is a claim, and provenance is the evidence for it.
Anything with an event attached — a match-worn shirt, a film-used prop, a presentation piece.
Anything frequently faked. The harder an object is to authenticate from the object alone, the more its history is doing the work.
What actually counts as evidence
A photograph of the moment. Somebody signing it, wearing it, holding it. The strongest thing there is.
An unbroken chain. Bought from X, who got it from Y, who was there. Each link weaker than a photograph, but a chain of plausible links is worth a lot.
Contemporary documentation. A receipt, a programme, a letter — dated at the time rather than written later.
A named expert's opinion, which is worth exactly as much as that expert is.
What does not count
A certificate from an unnamed authority. A card saying "Certificate of Authenticity" with no issuer is a piece of card.
"From a private collection." True of everything.
A confident story with nothing behind it. Stories are free.
How to ask
Directly and without apology. "How do you know?" is a normal question in this trade and a good seller has an answer ready, including when the answer is "I do not — it came in a lot and I am selling it as unverified."
That answer is fine. A seller who says they cannot prove it and prices accordingly is being more useful than one who implies certainty.
What a refusal means
A seller who will not say where something came from has told you something. Bid as though provenance is absent, because for your purposes it is.
More: how to spot a counterfeit, judging condition on camera.