So being stable when talking about valence electrons means that the valence shell has been filled completely (or half filled). The valence shell meaning the outermost electron shell. Stability meaning that something is unreactive, that it won't engage in some kind of chemical reaction to reach a new state. And vise versa, something which is unstable is reactive and will engage in chemical reactions to reach a new state.
Valence electrons are the electrons in the outermost shell, or energy level, of an atom. For example, oxygen has six valence electrons, two in the 2s subshell and four in the 2p subshell. We can write the configuration of oxygen's valence electrons as 2s²2p⁴.
