The essence of Einstein's idea is like this: if a system is in some bound state with energy $-E_b$ with $E_b> 0$ (the threshold of the continuum band is taken as zero), and we drive the system somehow with frequency $\omega $, then the transition into the continuum is possible only if $\omega > E_b$.
But this is apparently wrong in the general case. For example, take the hydrogen atom in the ground state. If we apply an oscillating electric field $E \cos \omega t $, then if the strength of the electric field $E $ is strong enough, the electron can get ionized however small $\omega $ is. In the extreme limit, $\omega = 0 $, and surely the electron can tunnel into the continuum!
Anyway, the conjecture is that, possibly if the intensity of the light is strong enough, we can still get photoelectric effect with $\omega < \omega_c$?