Today I Learned

That varies a huge amount. It's not a genre, just a medium, and like any medium there are a wide variety of genres made with it. Studio Ghibli tends to make surprisingly thought provoking children's movies, often without real villains. Cowboy Bebop is a hard sci-fi show in a constructed world with a jazzy sound track, and was probably the inspiration for Firefly. Ghost in the Shell is the ancestor of all modern cyberpunk, but with the quirk of being from the (still sympathetic) perspective of government counter-terrorism agents. GitS also tends to be heavily philosophical. You've got slice-of-life feel-good shows like Azumanga Daioh and K-On. There are children's and teen's shows about saving the world, and brutal deconstructions of those shows aimed at adults; Sailer Moon -> Madoka, Getter Robo -> Gundam -> Evangelion (second round of deconstruction went hard), etc. Then you have the genre-busting quirky stuff, like Haruhi Suzumiya (which is fairly sane) or Kill la Kill (which is decidedly not).

There's probably something out there in that space that you'd love, but it's a good idea to start from a genre you already like and look at that rather than just going with whatever show is big right now. The stuff that got really big in the US, like Naruto or One Piece, isn't generally my thing, and that's probably what you've run into. If you want to try a movie, check out Spirited Away, Princess Mononoke, Akira, and the first Ghost in the Shell movie. If you want to jump straight to a series, Cowboy Bebop, Haruhi Suzumiya, Last Exile, Death Note, Ghost in the Shell: Stand Alone Complex, Darker than Black, Serial Experiments Lain, Attack on Titan, and Spice & Wolf are all good without being too out-there.

Can't be explained. Has to be experienced.

A few anime to watch... Akira, Spirited Away, Nausicaä of the Valley of the Wind, Princess Mononoke, and many more.

It's just another medium. One appeal, it's from a similar, but different culture, so a lot of the tropes are unfamiliar and values being pushed are different.

Compared to US comics, manga isn't stuck in the superhero genre. You get more variety.

Another appeal for a lot of Japanese media is the original creator(s) have more control over adaptions.

With the source material, at least for me as compared to western stuff like X-men, Superman, etc, is that one, it crosses all genres and appeals to all genders. Comic books for much of their existence were largely geared to a specific, very male audience, and it was made quite clear by their writing and the actions of people into comics at the time that other genders (and, to a certain extent, skin colors) need not apply to join the club.

Since I’m a girl, when I was a kid I got teased a lot for liking ‘guy stuff’ like Batman and GI Joe. The problem was, well, I liked action stuff for one, but back then there just wasn’t anything for girls. Hell, I remember them even taking Wonder Woman’s power away, because apparently women empowerment reasons?

Those comics were all written by largely out-of-touch white guys who had, shall we say, definite opinions of what a woman could look like and should act like. And as a woman, I was never impressed. Especially by the time I got to the hundredth drawing of a woman’s ass and legs framing a supposedly ‘serious’ scene.

Then I found manga, with all-women writing teams, and artists who wrote well-rounded characters of all genders and orientations (Sailor Moon had many adorable scenes between a lesbian couple, just to name one example). They drew women who were people. They were sweet, they were brash, they were rude and crass, they were funny. And who weren’t afraid to fireball their way out of trouble. Hell, they drew varied guys who were weak, strong, silly, spacey… they felt real, in a way that I’d never seen in western comics.

Another thing is that mangaka tell the story, their characters get a satisfying actual ending, and then the artist moves on to another story. None of this ‘Oh, the X-men found happiness and solved their problems! In our next comic, watch as everything goes back to the shitty status quo because we have no idea how to write different stories!’ or ‘Welcome to the 2,171st reboot of Superman, now with Extra Edge^TM (because we hear that’s all the rage with kids these days). And remember that this iteration specifically references that one part of reboot #1,023, so read that too (if you can find it lol).’

And the third thing for me is it was quite a bit more beautiful and fluid and varied than western animation. Especially in the case of the days of Too-Many-Pockets Rob and his wooden doll faces, or the small beady eyes of, well, every comic character ever. Anime and manga faces were much more expressive, the worlds more varied and creative, and they weren’t afraid to draw regular people as protagonists, without muscles bulky enough to make you think you were looking at a Macy’s parade balloon.

I briefly checked out the source material from Naoko Takeuchi, which demonstrates why her work is so well regarded, though I personally don’t fully grasp the appeal.

Which is fine, I just don't understand manga/anime.