The octet rule states that elements gain or lose electrons to attain an electron configuration of the nearest noble gas.

Incomplete Octet

There are certain atoms of certain elements that can exist in stable compounds forming bonds with less than eight valence electrons. When this occurs, the atom of the element within the molecule is said to contain an incomplete octet.

The common examples of such elements are hydrogen (stable with only 2 valence electrons), beryllium (stable with only 4 valence electrons) and boron and aluminum (stable with only 6 valence electrons). For hydrogen 2 valence electrons give it a noble gas structure (like He) so this is much like the octet rule for everything else below period 1.

Expanded octet:

Expanded octet occurs when an atom is able to have more than 8 valence electrons. For example, in SO₃, the sulfur atom forms 6 covalent bonds, hence it has 12 valence electrons. Expansion of octet is possible only from Period 3 elements onwards, due to the presence of low-lying empty d orbitals that can accommodate the extra electrons.