The lowest visibility an airliner can land in is 300' RVR (runway visual range), that's not much. That is referred to as a Category III approach. To do that the runway first has to be certified for that which means the appropriate lighting and the ILS (instrument landing system) has been certified for that. O'Hare has multiple runways certified for that, Midway does not so operations at O'Hare can continue in worse weather than Midway. There are also multiple other requirements, the airline has to be certified to do Cat III, the airplane itself has to be Cat III capable, and the aircrew has to be trained and current to do Cat III approaches. Not all airlines pay for the equipment and training to do Cat III, and not all that are Cat III certified can go all the way down to 300' RVR, some have the minimums higher. Some airlines will be able to land at an airport in weather conditions that will force another to divert. Even different airplane types within the same airline will have different landing minimums.
On a real, no kidding 300' RVR approach you generally won't see the runway until you're about 2-3 seconds from touch down. The autopilot is flying it and the pilots are monitoring everything closely. It's a bit hairy but it works.
With O'Hare being capable of lower visibility operations than Midway it explains why they kept operating when Midway was closed.