clay: cheap potter's earth, the breakable material of ordinary pottery set over against metal
This word turns up in one place only: Nebuchadnezzar's dream of the huge statue in Daniel 2, and Daniel's explanation of it. Gold, silver, bronze and iron make up the figure from its head down to its shins. Then the feet arrive, and part of them is not metal at all but common baked earth, the material of jars and cooking pots. A reader in the ancient world would have felt the drop in value at once.
Everything the passage does with the image depends on what that material is like. Fired earth is hard, but it is hard in a way that breaks. It carries weight well and then shatters under a blow, which is exactly what happens when the stone strikes the feet and the whole statue is ground to powder and blown away. It also refuses to bond with metal: you can press iron and clay together, but they never become one substance, and Daniel says the same of the marriages and alliances by which the last kingdom will try to hold itself together. So the material is carrying the argument of the vision, one part strong and one part ready to crumble.
Which kind of clay is meant is a fair question, and the passage answers it as it goes. In Daniel 2:41 the clay is called a potter's clay, and twice it is paired with the ordinary Aramaic word for wet mud (טִין). The word's relatives in the neighboring languages mean a potsherd, a fragment of fired pottery, which is why some English versions read "baked clay" here instead of plain "clay". Hebrew keeps the two ideas in separate words: חֹמֶר for the soft clay on a potter's wheel and the mortar packed between bricks, חֶרֶשׂ for the fired result and the shards it breaks into. This Aramaic word sits nearer the second and lets the sentence supply the rest.