You know the familiar setup: Strong light source behind a wall with two slits in it, electron passing through. If the photon encounters the electron after it's passed through hole 1, then the electron acts as if that's the only path it took and the interference pattern is ruined; same for if it passes through hole 2.
If you only illuminate one of the slits, then any electrons passing through that slit will be disturbed, of course. So they then behave as if they passed through just one of the slits, and there is no interference pattern.
But if the electron passes through the slit that isn't illuminated, no direct observation is ever made on the electron. Because no flash of light occurred, we can deduce the electron almost certainly went through the non-illuminated slit. How did the electron "know" the other slit was being observed- and thus to act accordingly- if it's behaving as if it never went through that slit? How could that information be communicated to it?