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Quick Answer.  Noble gases are unreactive because their outer electron shells are full and therefore in their most stable state. Normally, elements react with one another because they have incomplete electron shells. They lose, gain or share electrons in order to gain a more stable electron configuration.
At the top of the noble gases is little helium (He), with a shell that is full with only two electrons. The fact that their outer shells are full means they are quite happy and don't need to react with other elements. In fact, they rarely combine with other elements. That non-reactivity is why they are called inert.