In the numerator we have the transition dipole moment for the  transition, whose squared amplitude represents the strength of the interaction between the electromagnetic field and the atom, and  is the vector electric field amplitude, which includes the polarization. The numerator has dimensions of energy, so dividing by  gives an angular frequency.
By analogy with a classical dipole, it is clear that an atom with a large dipole moment will be more susceptible to perturbation by an electric field. The dot product includes a factor of , where  is the angle between the polarization of the light and the transition dipole moment.  When they are parallel  the interaction is strongest, when they are perpendicular there is no interaction at all.
If we rewrite the differential equations found above:
and apply the rotating-wave approximation, which assumes that , such that we can discard the high frequency oscillating terms, we have
where  is called the detuning between the laser and the atomic frequencies.
We can solve these equations, assuming at time  the atom is in  (i.e. ) to find
This is the probability as a function of detuning and time of the population of state . A plot as a function of detuning and ramping the time from 0 to  gives:
We see that for  the population will oscillate between the two states at the Rabi frequency.