I sometimes see people ask why so often characters in a comedy anime will explain a joke after it’s happened, as the idea of doing so is, at least in English, considered a sure-fire way to kill any and all humor (I call it the Jay Leno Effect). I’ve been doing a bit of reading about Japanese humor recently though, and based on it I think I have a better understanding of why this happens.
Japanese social interactions are loosely governed by two concepts: “honne,” or one’s true feelings, and “tatemae,” what one displays outwards to the public. While I think it’s a mistake to put too much stock into this distinction (believing Japanese people cannot express themselves is sort of ridiculous), the explanation I’ve read is that honne and tatemae are central to certain types of Japanese humor, particularly manzai comedy. In manzai, the idea of having the boke (fool) and the tsukkomi (straight-man) is that the boke does something or says something ridiculous, and the tsukkomi responds with a sharp retort and/or a wack in order to correct the boke.
When it comes to anime, I think that actually when another character “explains the joke,” it’s not to tell the audience in case they didn’t understand. The idea is that something so unbelievable just happened that, rather than letting it slide and preserving the situation (tatemae), the person feels compelled to express his or her true feelings about it (honne). Essentially, the act of explaining the joke is part of the humor itself, as it essentially shows how the event was so jarring or absurd that the character had no choice but to tell it like it is. Sometimes you see characters in anime do this silently, taking advantage of the fact that the format allows us to be privy to their inner thoughts.
Of course, not all jokes can be explained by this, and in fact I’ve also read that some Japanese humor is about being able to create laughter on the inside without it spilling outside, which might explain certain slice of life humor like Hidamari Sketch and Yotsuba&! and the like. That said, I find myself laughing out loud at both of those titles pretty often, so who knows.