Orbitals, the regions around an atom’s nucleus likely to be occupied by electrons, are grouped into subshells identified by energy level (1, 2, 3, 4 and so on) and orbital shape (s, p, d, and f).
The 3d subshell contains five orbitals, each able to hold up to 2 electrons, a total of 10 electrons if all filled. Transition metals have stable ions with only a partially filled 3d subshell, and the five d-orbitals are degenerate, meaning they all have the same energy.
Crystal Field Theory describes how when a transition metal ion bonds with a ligand to form a transition metal complex, electron repulsion causes the d-orbitals to become non-degenerate, separating into two different energy levels. As the subshell is not full, electrons from the lower energy level 3d orbitals can jump to the higher energy 3d orbitals by absorbing visible light. The light absorption during these d-d energy transitions accounts for the characteristic vivid colours of transition metal complexes.
As the frequency of light absorbed corresponds to the energy difference between levels, what we see is distinct color corresponding to the remaining visible light frequencies not absorbed.