Question

Why do transition elements exhibit such a variety of coloured compounds, complexes and different oxidation states?

Answer 1

because their outermost shells are incomplete

Answer 2

transition-metal ions form coordination complexes because they have empty valence-shell orbitals that can accept pairs of electrons from a Lewis base. Ligands must therefore be Lewis bases: They must contain at least one pair of nonbonding electrons that can be donated to a metal .

The ability of the transition metals to exhibit variable valency is generally attributed to the availability of more electrons in the (n-1)d orbitals which are closer to the outermost ns orbital in energy levels.