The answer is simple: their atoms, or molecules that make them up, are closer together, so they can transfer energy between them much more efficiently. The particles of a solid are packed together tightly in a ordered fashion. There is little movement between them. The particles of a liquid have a little more freedom, being able to glide over and past each other, but are still relatively close together, so passing energy is easily accomplished. The particles of a gas are spaced far apart. For them to transfer energy, they have to bump into each other, which doesn't happen as much as it does for solids and liquids.
Think of it like this: which would be easier, in terms of forming an old-fashioned "bucket brigade" to pass a bucket of water, having 100 students shoulder to shoulder, passing the bucket, or having 10 students, covering the same distance the 100 covered? It would be much easier with the 100 transferring the bucket, one student at a time.