The outer shell of any atom seeks to have a completed orbital – that is, one with all the spots for an electron filled up. In all atoms after element #6, this means they want to complete the octet – the eight-electron outer valence shell.
The electron shells count outward from the nucleus, so that the one closest to the nucleus is #1, etc. The number of electrons that can make up a shell is equal to 2n2, with n being the number of the shell. For this reason, all the lightest elements tend to deal with an octet on the outer shell, or the lack thereof. Because heavier elements put their electrons in subshells, they also still tend to have an outer shell with eight electron slots.
If this eight-slot shell is not complete (making it an incomplete octet) it will seek to be filled or empty; this tendency is the single property that makes chemical combination possible. Elements with two electrons in the outer valence shell bond readily with elements that have six in the outer valence shell; the first element donates its two electrons to the element that can complete its octet with two more electrons.
Though the entire chemical process is much more complex than this, the simplicity of the incomplete octet and its workability makes it simple for scientists to determine what will and what will not combine easily.
Web Resources On Incomplete Octet
The Structure of Atoms and the Octet Theory of Valence
Book Resources On Incomplete Octet
Elementary Atomic Structure by G. K. Woodgate
Interfaces in Materials: Atomic Structure, Thermodynamics and Kinetics of Solid-Vapor, Solid-Liquid and Solid-Solid Interfaces by James M. Howe