Echoes Tang poet Liu Yuxi (刘禹锡), 《柳花词》: '发人无限思' - 'stirs in one boundless thoughts.' The modern four-character form crystallized from this poetic image.
usage
Used to praise something - a film, speech, book, question - that provokes serious reflection. Typically acts as a predicate after the subject (这番话 / 这个故事发人深思) rather than as a modifier.