apocryphal describes a story, quotation, or attribution of doubtful authenticity — widely repeated and plausible enough to pass, but unverified and probably not what it claims to be.
The everyday sense is a judgement about provenance rather than about content. An apocryphal anecdote is not simply a false one: it may well be true, and what it lacks is a source that can carry it. The characteristic apocryphal item is the famous line no one can trace to a first utterance, or the origin story that gets better with each telling. Such items survive precisely because they are too good to check, which is why deflationary phrasings like "the possibly apocryphal story that" have become a standard hedge in writing that wants the anecdote without vouching for it.
The older sense is scriptural: of or resembling the Apocrypha, the writings of contested canonicity that sit outside the accepted canon, retained in some traditions and excluded from others. That noun is the parent of the adjective, and the general sense grew out of it by extension.
Both words came through Late Latin apocrypha (scripta), "hidden writings," neuter plural of apocryphus, from the Greek apokryphos, "hidden, obscure," built from apo-, "away," and kryptein, "to hide" — the root behind crypt and cryptic. Apocrypha entered English in the late fourteenth century for the biblical books; apocryphal is recorded from the mid-sixteenth, and its use for non-scriptural material of doubtful authorship followed later. The word is weaker than spurious, which asserts that a thing is false or falsely attributed, and it differs from 📝myth, a traditional story whose function does not depend on being verifiable at all. An apocryphal tale merely goes unvouched for.