When running the dishwasher, water is coming out of the overflow on the kitchen sink. What is causing this to happen?

You have a clogged drain pipe, do you have a garbage disposal installed, see the image below remove the hose between the air gap and the G/D clean the hose, check the port of the G/D where the hose connect that knock out plate removed, install the hose and see if your problem is fixed, Thanks.

John