What Forer's demonstration exposed became known as the Forer effect, or, drawing the same point from an older showman's reputation for having something for everyone, the Barnum effect: people readily accept a vague, generally flattering personality description as a specific, personally accurate reading of themselves, especially when told an authority has prepared it just for them, and especially when the description leaves room for the reader to supply their own confirming details. The effect does not depend on the description coming from astrology specifically, though Forer's own sketch did; cold readers, personality tests, tarot readers, graphologists and generic corporate feedback forms all trade, knowingly or not, on the same mechanism.
Because the effect predicts that almost any vague positive description will feel personally true regardless of its actual source, it has become the standard skeptical tool for explaining why divinatory and pseudo-diagnostic systems report such high satisfaction from their clients without that satisfaction constituting evidence the system itself works. Psychologists studying astrology, tarot and personality profiling routinely cite Forer's 1948 demonstration, still the most replicated single experiment in the psychology of belief, as the baseline any claim of a system's real predictive accuracy has to be measured against and rule out before it can be taken as more than an artifact of how readily people accept flattering vagueness as insight.