Blue colour of copper complexesWatch
You want to scroll down to the subtitle: The nature of the ligand
It's a bit further down but if I were to paraphrase the explanation:
Different ligands affect the orbitals differently due to electrical fields. The electrical fields produced the dictate the gap between the split orbitals. As the electrons become excited and absorb a certain wavelength (thereby reflecting the rest giving your blue colour) at different levels, the shades of blue change.
So with your example, a normal copper complex with water has your cyan/light blue complex, that is absorbing red light. The complex with ammonia however leads to yellow light being absorbed, thereby reflecting your royal blue colour. Ammonia as you'll see in the diagram has a larger splitting potential than water (as a ligand) so the orbitals are split further apart. Remember, across the spectrum, energy corresponds to shorter wavelengths: red, orange, yellow etc. so more energy is being absorbed to excite the electrons.
I assume that your question is 'why are copper complexes blue?'
When ligands form coordinate bonds with Cu2+ ions, the d orbitals are raised to a higher energy level as there is repulsion between the electrons from the ligands.
In tetrahedral complexes (such as [CuCl4]2-) three of the d orbitals are raised to the same, higher energy state while the other two d orbitals occupy a lower energy state (which is still higher than the ground state when no ligands were bound to the Cu2+ ion). In octahedral complexes, it is the other way round, two of the d orbitals are promoted to the higher energy state while the other three occupy the lower energy state.
In either case, this creates an energy gap. When white light is incident on the solution, the electrons in the d orbitals absorb photons (light energy) which have energy that is equal to the difference in energy between the higher and lower energy levels. This energy, e is equal to the planck constant multiplied by the frequency of the photon. (E=hv, where h=planck constant and v=frequency of photon). The electron in the lower energy level will absorb the photon of a particular frequency and move up to the higher energy level. This frequency gives rise to the photon that has energy equal to the energy gap between the d orbitals.
The remaining frequencies of light superpose (combine) and form the complement of the colour that was absorbed, so in the case of Cu2+ ions, this is blue. The energy gap in Cu2+ complexes is such that the electrons in the lower energy state absorb light which is the colour that is the complement of blue light.
Hopefully this helps.