Basically it comes down to how easily or frequently particles can bump into each other, thereby transferring their energy.
In metals, the free electrons can zip around between atoms, bringing energy with them. In other solids, the atoms just have to bump their neighbors. And in e.g. wood, there’s actually a lot of tiny air pockets between the solid parts. It takes a lot longer for gas particles to randomly bump into each other than tightly packed atoms in a solid.
One final thought: if heat transfer were instantaneous, then everything on earth would instantly fall or rise to the average temperature of the whole. There wouldn’t be “hot” or “cold” things, there would just be one temperature for everything. Of course, because some heat is radiated as light (mostly IR), we’d lose it all to space, instantly. Also the heat death of the whole universe would happen instantly.
Aren’t you glad that it takes so long to preheat a skillet?
Think of heat transfer like shooting a pool ball into a group of other pool balls that all have a slight gap between them. One pool ball bumps into another one, which bumps into another one, and so on and so on. These pool balls are moving very quickly, but there are a bajillion of them, so it takes time to travel from one end to another. The denser the material, the closer the pool balls are to each other, so it takes less time to transfer the energy from one end to another.
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