I see Superflat (the term was coined by Takashi Murakami, I don't know if the aesthetic movement actually exists) is a kind of perverse self-parody of otakuism and the "database/modular" 2D visual culture. Basically it observes a move away from narrative content and into a kind of purely aesthetic gratuitous composition of pretty much identical elements (look at any range of character designs and you'll see how the characters we worship are built out of repeating iconographic elements, a lot like the way religious icons were designed in history, so that anyone could draw them.)
Murakami pokes at this kind of "deification" directly with his giant, larger-than, life pvc figures (kind of).
The basic idea of Murakami's Superflat Theory is to recognise an aesthetic system which is completely divorced from notions of "high" and "low" forms of art, in the similar ways that anime Otaku tend to embrace extremely shitty shows (by conventional aesthetic standards) because of otakuism's own standards and the database elements at play, as well as the show's meme-like cult personality.
It's not a very clear movement, but I guess it's exciting because it's young and radically different from how art has been made over the last century. In many ways it has more in common with older forms of Japanese art; ukiyo-e with its mass-produced, flat-graphic, cartoon elements (not to mention some of the sexual, moe paralells with some ukiyo-e artists) so it tends to attract a kind of Orientalist attitude which I don't much care for. The people most qualified to talk about Superflat seem to be the Otaku themselves, and they tend to have a hard time talking about it since they're so defensive.
But if you look at the broader picture, you can consider a lot of mainstream animated series today especially as being "superflat" in that they tend to no longer interface with original narrative content but feed off of otaku elements and otaku output in a kind of symbiotic relationship. A Kyoto-Animation (a fairly unapologetic creator of otaku content, like Gainax was) adaptation of a show like Haruhi or Lucky Star (I'm using these shitty examples because they're popular) with their self-conscious fan-service and inter-lacing of genres/archetypes I think might illustrate how their already isn't much of a divide between what Superflat illustrates in the Art World (that horrible place) with what's actually going on in the Otaku subculture, which is where "Superflat" (if we can call it that) is actually living and breathing.
you can pretty much look at any otaku series today and see similar examples of "flatness" a lot of fans might complain of these shows as "fanservice shows" with no souls, and that's just the point, traditionally transcendentally important elements of the art-form like "Story" are designed to be as basic fan-service like pornographic aesthetic enjoyment as the panty-shots and cute character designs. So Story is basically used as much as a vehicle for character design as visa-versa, and as far as otakuism is concerned that's how it should be.