The text is a twist on the common phrase 'He who laughs last laughs best', which means that the person who understands and reacts to a situation last may actually have the best understanding of it. The twist 'had to have it explained' humorously suggests that the reason for laughing last is not understanding the joke initially, rather than having the best understanding. This relies on the subversion of expectations rather than a play on words or similar-sounding words.
He who laughs last . . . had to have it explained .