My dishwasher does not work and water backs up into it can I plug the hose that goes to the washer. Is the hose to the washer some type of airsystem for disposal

The drain has either a "high loop" or an "air gap". The air gap sits on the sink, the "high loop" just makes the drain go significantly up before it comes down. They both prevent cross-contamination.

The water line is just a water line. Why not just turn off the water to the dishwasher?