Why are deserts hotter than other places on Earth
We all know that deserts are the hottest places on Earth.

That is not necessarily true. What is true is that the hottest places on Earth are in deserts. Note the reversal. Much of the Arctic and Antarctic are technically deserts due to extremely low precipitation. Excluding these polar deserts, some deserts are quite cool, even if they are close to the equator. For example, Arica, Chile (the driest inhabited locale in the world), has a rather mild climate temperature-wise, despite being at 18°29′ south latitude. This is the case for much of the Atacama desert.


What makes them different from other parts of the world?

I'm assuming you are asking about those deserts that are hot in the summertime rather than deserts in general. A key ingredient for extremely high temperatures is a desert, but not a high latitude desert, high altitude desert, or coastal desert.
Very low precipitation is what distinguishes desert from non-desert biomes. Lack of precipitation is not sufficient for very high temperatures, as exhibited by the very cold polar deserts and the rather cool deserts that are well outside polar areas. Much of the Atacama is at a high altitude, as are the Gobi in China and Mongolia, the Taklamakan in China, and the high desert in the Mexico and the US. While some of these deserts can be hot during summer, they aren't ridiculously hot. Areas along the coast of the previously mentioned Atacama desert and the Namib in Africa are kept somewhat cool by ocean breezes. These coastal deserts can be uniformly mild year-round.
What is needed to create the possibility for extremely high temperatures is a desert that is not at extreme latitudes, that is well removed from coastal cooling, and that is at low altitudes. A desert is needed so as to receive the full brunt of solar radiation. Equatorial regions don't work because they tend to be cloudy and rainy. High latitude areas don't work because they don't receive very much insolation. High altitude areas don't work because temperature tends to decrease with increased altitude.
A low altitude desert in the horse latitudes is exactly what is needed, and this is why Furnace Creek in Death Valley, California (supposedly the hottest place in the world) and Tirat Zvi, Isreal (supposedly the hottest place in Asia) can be very, very hot. The horse latitudes are where the Hadley cell and mid latitude cell converge, creating long-lived high pressure areas where rain is highly unlikely. Most of the world's non-polar deserts are in or near the horse latitudes.
Even better than Furnace Creek are those areas that are so ridiculously hot that nobody sane would live there and hence there are no weather stations. We don't know, for example, how hot it gets in the Lut desert in Iran. It's too hot there for people to fathom, and is almost certainly hotter than is Furnace Creek.