For example, consider carbon which has electron configuration 1s2 2s2 2p2.
If we were to populate the 3 p-orbitals with two electrons with spins either up or down, which has more energy? E.g. of the following two:
m_L -1 0 1 u_ u_ __ u_ __ u_ __ ud __
Higher spin multiplicity means lower energy. I.e.: you want to keep all spins pointin in the same direction.