Okay, FLCL is like the coolest thing, ever.
Being an OAV by Gainax, the creators of Neon Genesis Evangelion, comparisons between FLCL and Eva are natural. Eva was a grander, more ambitious project, with arching storylines and heavy Judeo-Christian metaphors. FLCL, on the other hand, while not exactly whimsical, has a better sense of humor and carries a lot less emotional baggage. The characters are more straightforward, without the hidden agendas and closet-stuffing skeletons of Eva. After all, it is only six half-hour episodes long.
Naota, the lead in FLCL, is essentially a younger version of Eva's Ikari Shinji reimagined with more testicularity and self-assurance. He's also much more astute when it comes to appreciating the bizarre events surrounding him and understanding the motivations of the people in his life. He's also much more resigned to his fate, whereas Shinji never missed an opportunity to waver or whine.
Actually, I guess Naota's not really much like Shinji at all, except for the fact that he is a young boy forced to accept fantastic responsibilities and faced with mad circumstances beyond his control. Like Shinji, Naota's world is one largely shaped by the various women in his life. In that sense, Naota and Shinji, in their own uncertain sort of way, echo Tyler Durden's views on the challenges to expressing masculinity when the immediate influences in their lives are predominately female. Both Naota and Shinji respond to this frustration through their performances as reluctant robot pilots, although Naota is more successful than young Ikari in defining himself outside of this station despite the fact that the male role models available to Naota (his father, grandfather, and the guy with the eyebrows) are essentially worthless. Nevertheless, Naota, in his epilogues, demonstrates a mature resignation and understanding that belies his frantic posturing and completely escapes Shinji's gutless desperation.
Thematically, FLCL is much more straightforward than Eva, despite the fact that both shows rely heavily on symbolism. The sexual metaphors in FLCL are obvious, but (for the most part) tastefully executed.
Perhaps the most obvious difference lies in the emotional content. All of the characters in Eva (except Ayanami Rei, arguably) are generally unhappy, whereas the leads in FLCL are generally glad for their adventures, despite the troubles they produce.
Unfortunately, it's not really possible to describe what the show is about in a way that does justice to its brilliance. My Not Quite Yiddish NoCal Friend aptly called it "basically a perverted Mary Poppins, coming-of-age story with some robots thrown in." That's about as good a nutshell description as I can come up with.
Frankly, I consider the plot to be a rather trivial element largely unnecessary in the appreciation of FLCL.
If you must know, Naota, a twelve-year-old boy, is walking home with his older brother's girlfriend, Mamini. An older girl, Haruko, comes out of fucking nowhere and drills him with her Vespa, then clocks him in the head with her gas-powered bass. Haruko ends up sharing Naota's bedroom while serving as his family's housekeeper. Then the robots show up and it starts getting weird.
But really FLCL isn't about robots or aliens or thinnly veiled erection metaphors, it's about style and flash and music. FLCL swirls in a St. Vitus' Dance of visual and stylistic changes evoking anime standards, manga art, and comic book staples with a little bit of South Park, the Sunday funnies, and Schoolhouse Rock thrown in for good measure. Driving it all are the underlying alt-rock, punk riffs of The Pillows, joyfully and enthusiastically echoing Naota's resignation, Mamini's irreverence, and Haruko's subversiveness.
All in all, it's like the coolest thing ever.