What are ω and ν in this expression?
$\Delta G_m$ is the free energy barrier for the motion of atom from one site to another. The equation overall looks like a transition state approach to this activated process, and thus $\nu$ is the frequency at which this motion is attempted, i.e. a $\nu$ is a characteristic lattice frequency. In such models, it is often assumed to equal the Debye frequency.

Finally, $\omega$ is the rate of transition from one site to another, or something proportional to it (because the proportionality symbol is used rather than an equality). $\omega$ can be thus be the ionic conductivity, or a diffusion constant.

You can find the same expression and graph in this chapter of undergrad lecture notes, for confirmation.