There is a rather insightful, complete writeup about the book Going Postal above, so my comments will instead feature a few thoughts on where the book sits in the Discworld corpus in general. All of the Discworld novels can be read on their own, but the more that are read, the more the overall themes of the series come through.
Discworld is a series of books by Terry Pratchett about a fictional, fantasy-themed world set on a disc carried on the back of four elephants, which are in turn carried on the back of a gigantic turtle, swimming through space. Going Postal is a book about the establishment of the post office, the role of monopolies in capitalism, the internet and libertarianism. Someone who has read many of the Discworld books thinking "yes, yes, what is your point". The non-familiar reader may think those two statements are somewhat incongruous, which shows that perhaps they have an advantage in this point.
The Discworld books started out as a parody of fantasy themes. It was actually this reputation that kept me away from Pratchett for so long, I thought his works would be similar to Piers Anthony, repetitive in-jokes on fantasy for the those who appreciated such in-jokes. And the early Discworld books were somewhat in that line. In my opinion, the early books were both less funny and less involving then the later books. Over the course of the books, a few things happened.
The fantasy setting used to be there mostly as backdrop for whatever the story of the current book was. It was more one-dimensional, and being one dimensional, less humane. The residents of Discworld's largest city, Ankh-Morpork, were an easily manipulated proletariat, at the mercy (such as it was) of the Thief's Guild and Assassin's Guild. The wizards were an amoral, fratricidal lot. The ruler of the city, The Patrician, was a vicious tyrant who would assassinate or torture anyone who got in his way. The anthropomorphication of Death was a cruel spectre. of But as the series went on, two things happened: fantasy tropes exhausted their amusement as sources of mockery, and Pratchett, writing about the same characters over dozens of books, coudln't treat them one dimensionally. He started showing some affection for his characters, and started solving their problems, instead of just cynically commenting on them.
It would be hard to say when that started happening, but by 2004, and "Going Postal", the transformation is almost complete. The fantasy underpinnings of the world are not explored. There is still magic mentioned, but it is just a supporting point. The Patrician, once a Machiavellian figure, is recast as someone protecting the little people of Ankh-Morpork from those who would exploit them, and who uses his knowledge of human nature and veiled threats to get his way, instead of total cruelty. One of the ways he does that is to manipulate the book's protagonist, Moist Von Lipwig into taking care of the postal service to undermine the monopoly of The Clacks, a telecommunication monopoly. Lipwig's struggle with his criminal nature, and the discussion of corporate financing and the downside of libertarianism, is a much more involving, and humane plot than was present in the earlier books. The portrayals of the supporting cast members, such as Stanley, the autistic boy who collects pins, and Tolliver, the gruntled old man with dangerous natural cures for his ailments, are also not the stuff of fantasy trope, but are instead commentaries on contemporary society. The focus of the books is no longer on fantasy, but on the evolving civic life of Ankh-Morpork.
All of this explanation is perhaps giving the wrong impression of the book. The serious content, and turn in thematics, has not made Pratchett's writing style more dry. This book zings along with odd, yet fitting descriptions of people and places, as well as the typical Pratchett mystery with attendant plot twists and turns. While the book can be read as part of the Pratchett corpus, it can also be read as a funny story of a man trying to run a post office in a world much like ours, only exaggerated for comic possibility.