Seinfeld was both smart and down-to-earth, so it appealed to a really broad audience. The American sense of humor is unique. I typically find British humor much funnier, but Seinfeld is still my favorite show of all time. Number two is Faulty Towers, an older British gem of a show that few Americans have even heard of. The only other American sit-com I really loved was Martin, which was underrated (at least among whites) but really just owed its genius to Martin himself and all his insane characters, as the rest of the cast wasn't all that funny with the exception of peripheral characters like “Bro Man.” But having only one funny character was typical in sit-coms, even good ones like Martin. They also had very simple plot-lines, usually involving some misunderstanding.
Seinfeld, on the other hand, for a show that was supposedly about nothing, in each episode tended to have quite a complex plot structure, especially for a half-hour sit-com. It wasn't just a, then b, then c. It was several different storylines interwoven, with seemingly small occurrences in the beginning suddenly becoming vital to some hilarious incident later on. Someone smart was taking care, and writing these episodes with the thoughtfulness an author would use in developing a novel's plotline. I'm not saying these episodes were like fine novels--I'm just saying the same type of attention to detail and plot development was being used on a smaller scale, and with comedic intentions instead of dramatic ones. But as a literature/English student, this show had actual, authentic, complex and admirable structure in its story/plot development. That's why it was captivating to so many people, even if they may not have thought of it in those terms. I can't think of another comedy that has (even since then) taken such a high-minded and interesting approach to plot/story development.
The show was similarly bright and forward-thinking with its character development and how they interacted. Each character had a unique comedic presence: Jerry had witty observations, whereas Kramer used mostly physical humor, whereas George's humor was based in neuroticism, and Elaine's in dry cynicism. Even George's parents or the infamous Newmann had their own crazy humor/quirkiness. Few writers could accomplish this feat, as other sit-coms use one style of humor painted with a broad brush on all the characters, for the most part. This interaction on Seinfeld between these very different characters was what made the show so rich and brought the complex plotlines to life.
Finally, the subject matter, which was basically a self-reflective, tongue-in-cheek look at American culture, had never been done before, that I know of. The show wasn't about nothing--it was about us, but only the superficial things we all know, have lived and can relate to. That's why it appealed to so many people. The show took everyday situations and made a whole episode about them, like getting caught picking your nose. It was ridiculous and superficial and, as another answer aptly pointed out--none of the characters were even likeable outside of being funny. But somehow it took all that and made a genius little gem of a world. I doubt there will ever be a comedy I view with the same reverence as Seinfeld!