When the visibility is very low, LVPs (Low Visibility Procedures) are enforced - this will be broadcast on the ATIS. Each airfield's different but this normally happens when the conditions approach the minimum for what's called a 'Cat I ILS' approach - at Gatwick, the Cat I minima are 550M runway visual range (essentially visibility) and a cloud base 200' above the ground, for the aircraft I fly.
The 200' is the decision height i.e. you must go-around if you don't have the required visual references on the ground at this point. We can hand-fly Cat I ILSs down to 200' then land if we can see the runway.
Our aircraft (medium twin-jets) are approved for Cat IIIB approaches (culminating in an autoland) - the minima for these are 75M and they don't have a decision height (!) so you can appreciate that the conditions can be very bad and aircraft can still land. The downside of LVPs is that they slow everything down - more space is left between aircraft, aircraft have longer final approaches, aircraft need to clear the runway by a greater margin than usual before other aircraft are cleared to land (due to the danger that the vacating aircraft will interfere with the ILS beams being used by the landing aircraft), etc.
As an aside, autolands tend to be quite a bit more, er, "positive" than hand-flown ones! You also tend to land a little longer if the autopilot's doing it.
B&S
