When electrons fill a set of orbitals that have equal energy, Hund’s rule applies. Electrons spread out into separate empty orbitals first, before any pairing happens. This keeps electrons as far apart as possible and lowers their mutual repulsion.
Forcing two electrons into the same orbital costs energy, called pairing energy, because both electrons carry negative charge and naturally repel each other. In transition metal complexes, chemists compare this pairing energy to another value called the crystal field splitting energy. Whichever energy is larger decides whether the complex ends up high spin, with more unpaired electrons, or low spin, with more paired electrons.
This idea of pairing underlies how chemists predict a substance’s magnetic behavior and how reactive it will be. A common misconception is that pairing is always unfavorable and something atoms avoid whenever possible. While pairing does cost energy to overcome electron repulsion, it becomes necessary once every available orbital in a set already holds one electron.
Whether a transition metal complex ends up high spin or low spin depends on several things. These include the specific metal, its oxidation state, and the strength of the surrounding ligands. This is why the same metal can show different spin states in different compounds.
This is one reason transition metal complexes display such a wide range of colors and magnetic behaviors across the periodic table.