What kind of electronic transition take place in the exhibition of colour by transition metal ions

Transition metals are coloured due to the d-d electronic transition.
It's a transition where an electron jumps from one d orbital to another. Normally these are degenerate (the d orbitals have the same energy), but under some conditions, such as the presense of ligands, the degeneracy can be removed so that there is a specific energy (and therefore wavelength) associated with these transitions. These sorts of transitions sometimes have energies located in the visible band, and it's one reason transition metal ions (and complex ions in particular) tend to be highly colored.