Crystal Field Theory concerns transition metal complexes, in which ligands (which are treated as point charges) approach at various coordinations (eg octahedral, tetrahedral, square planar), and as a result raise and lower the d orbitals in energy. This splitting of orbitals can be sufficient to pair electrons in some d orbitals before all are filled. This gives rise to 'low spin' and 'high spin' states (as observed in iron in haemoglobin).
The energy jumps betweeb the raised orbitals and lowered orbitals are in the region of visible light, giving the characteristic colours of transition metal complexes.
In answer to your question, copper is a d9 transition metal, which experiences the Jahn-Teller effect, which effectively distorts an octahedral complex so much that two ligands on the z axis are sp loosely held, that they depart, leaving a square planar complex.
Further reading: Greenwood and Earnshaw