The less reactive an atom is the more stable it is. Reactivity is based on how many valence electrons the atom has- 1 is the most reactive and 8 is the least reactive. If you get a sodium atom which has one valence electron and pop it in some water, the sodium will explode. However, if you put helium in water, nothings gonna happen because helium has full valence electron shells so it wont react.
Chemical reactions are basically just atoms trying to fuse together, so if the atom already has the optimum amount of valence electrons, its not going to want to share them or give them out. If its not giving out its valence electrons, its going to be stable since it wont try fusing.