Mr. Ceridwen once had a very large public tizzy about how irritating this book was to him, I'm sure made all the more irritating because I had also just publicly declared my enduring love for Mr. Miéville. That was probably like a dozen years ago, which is apparently how long it takes me to get over my amusement at Mr Ceridwen's annoyance. Far be it from me to actually read the book in question, because I might actually agree with him, and then a very good source of bickering would be ruined. That whole anecdote is probably more illuminating of my marriage dynamics than I would prefer.
But then it turns out I earnestly have no idea what his problem was! The eponymous cities of The City and the City are Besźel and Ul Qoma, which are something like Buda and Pest: cities divided by a river and topography, but ultimately bound together into Budapest. Except entirely opposite of that: Besźel and Ul Qoma occupy the same land, the same space. People can be walking down a street in one city and dodging people in the other. But this seeing and in seeing cannot be done obviously or delibrately; the cities unsee each other. The borders are fiercely maintained even though they are diffuse and internal.
The plot follows Tyador Borlu, a detective from Besźel, who picks up a murder case that appears to be a matter of breach: her murder appears to puncture the inviolate membrane between the city and the city. Breach is one of those things that terrify the denizens of those cities, and it's hard to tell if it's social prescription or semi-mystical woo-woo -- and this is what irritates Mr. Ceridwen. Borlu in his detective plot moves through both cities and between to find the girl's killer.
My take is more ¯_(ツ)_/¯. Why not both? The social contract is rigidly enforced in just about any city, be that city authoritarian or boho. People have hundreds of internal rules -- thousands -- about who they interact with and how, who they see and unsee. Its both entirely mundane and semi-mystical. To misquote a favorite poet: we live in imaginary gardens with real toads in them.