Desert Temples look like pyramids; they have stairs going to the top, a main entrance and a few hidden ones, etc.. They are constructed mainly of sandstone, and have wool. Underneath the blue wool is a pressure plate; blowing the whole structure up. A safe way to get down is to mine the wool next to the blue wool, since there isn't any pressure plate there. There are also 4 chests in the secret room, containing items and mainly some rotten flesh and bones, saying that people died down there. There are also sometimes golden ingots. Desert Temples are one of the most valuable structure, having the chests with valuables, and the blue wool and TNT to blow your friend up.
Desert Temples sometimes spawn in Desert Biomes, never anywhere else. In one, do NOT mine the blue wool and fall down; you will be blown up. To get down safely, mine the orange wool next to the blue wool. Then you can drop down safely. A good way to get down is to drop water down, thus destroying the pressure plate and making a safe way down.