As the characters in the show have referred to the show, Seinfeld is a show in which basically nothing really happens. There's no set goal for that characters throughout the series, and each episode's narrative focuses on day-to-day activities for a normal person, but featuring their dysfunctional actions and thoughts.
Seinfeld, for the most part, follows comedian Jerry Seinfeld and his close group of friends that are each struggling to get through adult life with their lack of social skills and general idiocies; Kramer, a character based on someone Larry David once lived near, is wholesome but always coming up with crazy money-making schemes and miraculously manages to stumble across financial gains, despite his overall lack of intelligence. George Constanza, based on Larry David himself, is a complete social screw-up and always getting into easily-avoidable situations due to his overthinking of things. Elaine Benes is probably the most normal of the group, coming from a well-off family and often being the voice of reason.
With the characters being close, easily recognisable and different in their own ways, it allows the excellent comedic writing of Larry David and Jerry Seinfeld to take over and throw them into the worst environments they'd consider. No need for a clear narrative, just throw a few inconveniences at the characters and allow their personalities to take over. It's an incredibly simplistic show, and that's exactly how it become so successful. Outside of the writing, the casting is perfect. The chemistry and friendships between the actors feels so natural, so authentic that it's hard to look at the actors without feeling as if they are those characters, living their chaotic lives and attempting to get by.
Seinfeld brings in a new form of storytelling, sticking almost entirely to character development. It's a refreshing, and enjoyable structure that resulted in a plethora of other sitcoms attempting to carry on that style -- Friends is a close competitor, but certainly not on the same level as Seinfeld -- and it's impressing that Seinfeld was capable of lasting nine entire seasons, with around twenty episodes per season.