What specific geological feature is shown in the background?

The geological feature shown in the background is Cape Creus, also called Cap de Creus.

The craggy rocks at the right side of The Persistence of Memory represent the tip of the Cap de Creus peninsula in northeastern Catalonia, Spain. Dalí knew this region intimately: he was born in nearby Figueres and spent important parts of his life around the Catalan coast, especially Cadaqués and Portlligat.

That landscape gave the painting a recognizable geographic foundation even though the foreground is dreamlike. The hard, sharply modeled rocks contrast with the melting watches, helping Dalí place impossible objects in a real Mediterranean setting. The shadowy form in the foreground has also been associated with Puig Peni, a mountain in the same northeastern Catalan area.

Barcelona, Figueres, and Cadaqués are related places but are not the specific geological feature depicted. Barcelona is a major city, Figueres is Dalí’s birthplace, and Cadaqués is a nearby coastal town; Cape Creus is the peninsula and rocky headland represented in the image.