The octet rule states that atoms tend to combine in such a way that they have eight electrons in their valence shell, based upon the chemical inertness of noble gases.

Its significance lies in the fact that it is quite useful for understanding the structures of most of the organic compounds and it applies mainly to the second period elements of the periodic table.

However, the octet rule is not universal and has several limitations. It is based on the chemical inertness of noble gases, but some noble gases like xenon and krypton combine with oxygen and fluorine to form compounds like XeF$_2$, KrF$_2$, and XeOF$_2$. Additionally, this theory does not account for the shape of molecules and does not explain the relative stability of the molecules, being totally silent about the energy of a molecule.

There are three main types of exceptions to this rule. The first is the expanded octet, where elements in and beyond the third period have 3d orbitals available for bonding, resulting in more than eight valence electrons around the central atom (e.g., PF$_5$, SF$_6$, H$_2$SO$_4$). The second is the incomplete octet, where the number of electrons surrounding the central atom is less than eight, especially in elements having less than four valence electrons (e.g., LiCl, BeH$_2$, BCl$_3$, AlCl$_3$, BF$_3$).

The third exception involves odd-electron molecules. In molecules with an odd number of electrons like nitric oxide (NO) and nitrogen dioxide (NO$_2$), the octet rule is not satisfied for all the atoms.