Warning: Wikipedia contains spoilers.
The story takes place on the fictional planet Urras and its moon Anarres. (Since Anarres is massive enough to hold an atmosphere, this is often described as a double planet system.) In the aftermath of a failed anarchist revolution, the rebels were exiled to the moon about two hundred years prior to the events of the story.
The protagonist Shevek is an anarchist physicist/philosopher attempting to develop a theory which will allow the construction of an ansible, a faster-than-light communications device, but his efforts are blocked by parochial and xenophobic attitudes in his home society.
He therefore embarks on the risky journey to the original planet seeking the conversation with other mathematicians and physicists which will bring his theory to fruition. The plot explores his struggles on the anarchist planet, as well as his struggles after he travels to the original planet.
The book also explores the Sapir-Whorf Hypothesis: on the anarchist planet the use of the possessive case is strongly discouraged. An example is given where a little girl says to Shevek: "you may share in the handkerchief that I use", rather than "you may borrow my handkerchief". The idea is that the handkerchief is not owned by the girl, merely carried by her. The language spoken in Anarres, Pravic, is a constructed language that reflects many aspects of the philosophical foundations of utopian anarchism.
The Dispossessed is considered by some libertarian socialists to be a good description of the mechanisms that would be developed by an anarchist society, but also of the dangers of centralization and bureaucracy that easily take over such society without the continuation of revolutionary ideology.
The work is sometimes said to represent one of the few modern revivals of the utopian genre, though it is notable that one of the major themes of the work is the ambiguity of different notions of utopia.
See also Anarchism in the arts