The transition dipole moment or transition moment, usually denoted {\displaystyle \mathbf {d} _{nm}}{\displaystyle \mathbf {d} _{nm}} for a transition between an initial state, {\displaystyle m}m, and a final state, {\displaystyle n}n, is the electric dipole moment associated with the transition between the two states. In general the transition dipole moment is a complex vector quantity that includes the phase factors associated with the two states. Its direction gives the polarization of the transition, which determines how the system will interact with an electromagnetic wave of a given polarization, while the square of the magnitude gives the strength of the interaction due to the distribution of charge within the system.

The answer above is the first paragraph of the Wikipedia article on “transition dipole moment”. That article covers the topic well and also has some very useful illustrations. That article will provide a better and more complete answer than can be written here.

To absorb or emit light a system must increase or decrease its energy state. In addition, since light is an oscillating electric field, in changing from one state to the other the system must produce an oscillating electric dipole. So it is the transition itself, the superposition of the initial and final states that must produce and oscillating electric field in order to interact strongly with EM waves, producing or absorbing them. The wiki article provides an excellent illustration of an electronic transition showing how the superposition of the initial and final states actually produces a state where the electron position is oscillating. The case for a vibrational transition is no different. The transition, i.e. the superposition of the initial and final energy state must constitute an oscillating dipole if the transition is to emit or absorb light.

Thank You Mike Albert The illustration indeed looks very intuitive.

Thank You Alliance Tony-Mayeko

I am also open to more answers or elaborations.