Basically, when Federico da Montefeltro was decorating his new palace, he commissioned a wonderful set of intarsia, mainly destined for his studiolo (study room). When not furiously waging war, he loved Greek literature and the liberal arts, and the designs chosen reflect this: scenes with 3D platonic solids, an astrolabe, an armillary sphere, musical instruments, animals (such as squirrels), etc. You can see some of these in this "Procrastinating in Pittsburgh" blog post (and in this one too): the amount of technique that was required to execute these small marvels is frankly incredible.
Other Quattrocento palaces commissioned similar intarsia works, such as this perspective view of a cittern (lute-like instrument) and sand-timer from the Palazzo Ducale in Gubbio (from 1479-1482).
But what I didn't know was that there was also a set of three cityscapes done in this same intarsia style: one is in Urbino, one in Baltimore, one in Berlin. These have been attributed to Luciano Laurana, but this is hard to be sure about.
What do they depict? Jockusch concluded (in a 1993 dissertation) that while some intarsia panels depicting real scenery did exist (one of Monte Oliveto near Siena, the other of the Colosseum in Rome), the rest - including these three - were all very probably imaginary.
OK, so what were they for? According to a 2007 study by Macerata University geography professor Giorgio Mangani, these were probably memory aids (the "architectural mnemonic" in the Ars Memoria, as discussed by Aristotle, Cicero, Thomas Aquinas, etc).
I haven't yet seen Mangani's study, but his conclusion seems a bit of a stretch to me. This article (part of Kim Veltman's 2004 work here) notes plenty of other views: Krautheimer (1948) thought the Baltimore and Urbino panels represented tragedy and comedy, though Sanpaolesi (1949) disagreed; while Battisti (1960) speculated that they might instead be visualizations of ancient cities.
It's a mystery - or is it? Do these three idealized cityscapes actually need to be for anything, any more than the squirrel or the astrolabe or the sand-timer? Perhaps Mangani is right and that someone used or appropriated them for their own personal mnemotechnical odyssey, but that seems a little after-the-event.
My personal preference in this instance is, in broadly the same vein as Charles Hope's skepticism about claims of Neoplatonism in art, that these are just perspectival grandstanding, 3d technique for its own sake. If there is an art history link to these cityscapes, it might well turn out to be to Antonio Averlino's ideal city Sforzinda: but even this I'm not really holding my breath for.