Answer:
The increased stability of the atom, most commonly manifested in a lower energy state, arises because the high-spin state forces the unpaired electrons to reside in different spatial orbitals. A false, but commonly given, reason for the increased stability of high multiplicity states is that the different occupied spatial orbitals create a larger average distance between electrons, reducing electron-electron repulsion energy. In reality, it has been shown that the actual reason behind the increased stability is a decrease in the screening of electron-nuclear attractions.[2] Total spin state is calculated as the total number of unpaired electrons + 1, or twice the total spin + 1 written as 2S+1.
As a result of Hund's rule, constraints are placed on the way atomic orbitals are filled using the Aufbau principle. Before any two electrons occupy an orbital in a subshell, other orbitals in the same subshell must first each contain one electron. Also, the electrons filling a subshell will have parallel spin before the shell starts filling up with the opposite spin electrons (after the first orbital gains a second electron). As a result, when filling up atomic orbitals, the maximum number of unpaired electrons (and hence maximum total spin state) is assured.
For example a p4 subshell arranges its electrons as [↑↓][↑][↑] rather than [↑↓][↑][↓] or [↑↓][↑↓][ ].