SPOILER: sent in by Martina who says... (condensing a 700+ pages book into a couple paragraphs is tricky, but I'll do my best)
This story is set in an alternate Britain at the dawn of the 19th century, a Britain where magic once was a powerful and everyday force but has since become extinct (or rather, misplaced). It is only known as a theoretical study until Gilbert Norrell proves that he has rediscovered the art, and he sets out to earn magic a prominent place in British society once more.
Distrustful and jealous of other potential mages' power, he nevertheless eventually takes a pupil, Jonathan Strange. Together they prove their worth to the government, but during the Napoleon Wars, when Mr. Strange is sent to the front while Mr. Norrell remains in London, they become estranged. They finally seperate over a quarrel about the Raven King, an ancient northern king of legends who, raised by faeries, was the one to bring magic into England. There is an ancient prophecy by the Raven King which seems to point to the two mages among other things, but they are as of yet unsure as how to interpret it (and Mr. Norrel, who despises the Raven King, dismisses it outright).
They now work towards seperate goals and, occasionally, against each other; this is further complicated by a third party, an ancient faerie king who was once secretly summoned by Mr. Norrell and who now has a door into the realm of humans again and both intentionally and unintentionally causes harm to humans, among them Jonathan Strange's wife, whom he kidnaps while letting the mage believe she died. Stephen Black, a human servant to whom the faerie king has taken a deep liking, tries to rein him in but in this is very rarely successful.
Jonathan Strange, travelling to ease his sorrow, now practices magic with even less caution than before, and manages, among other things, both to unleash magic to its fullest extent in Britain again and to get himself cursed into being surrounded by perpetual darkness by the faerie king. When he returns to Britain, he reunites with Gilbert Norrel and together they, while trying to contact the Raven King, happen to fulfill his prophecy, at least the parts about the second coming of magic and the rise of Stephen Black to a king of Faerie (the prophecy is not particularly easy to interpret, for the mages as well as the reader).
In the end, Gilbert Norrel has too been captured by the curse on Jonathan Strange, so they set out together to discover new places of magic now that it has returned to full strength, while Arabella, Strange's wife, freshly rescued from the faerie kingdom, stays behind in England to wait for his return. Meanwhile, new mages in Britain form new guilds, calling themselves Norrelites and Strangeites depending on whose perspective on magic they follow.