What are inactive gases?
Inactive gases are gases that are chemically unreactive.
A look at the periodic table shows that these gases are (in order of increasing atomic number) Helium, Neon, Argon, Krypton, Xenon and Radon. They are all grouped together in one vertical column because they tend to share the same chemical properties.
Chemical properties are entirely determined by the the way the electrons are arranged in orbit around the nucleus of an atom. All chemical reactions involve the transfer of the outermost electrons across the various substances involved. It turns out that the most stable electronic configuration is reached when the outermost shell of an atom holds the maximum number of electrons it can accommodate - eight electrons.
All the gases listed above (except Helium) have eight electrons in their outermost orbital, thus making them very unreactive. Helium has just one orbital which can only hold two electrons. Because this orbital is fully occupied it renders Helium unreactive as well.