A dishwasher air gap sits in between the drain hose and the end point where the water drains out (typically the garbage disposal). Some people don’t install an air gap and instead just connect the dishwasher drain hose directly to the garbage disposal inlet. That’s a no-no.
It is not difficult to install an air gap for the dishwasher. You will need about $20 in parts and about an hour of your time.
You will need the air gap itself, a hose that runs from the air gap to the dishwasher, and a handful of hose clamps to hold everything together. Ideally you need a hole in your sink or countertop for the air gap to sit (although some people will just attach the dishwasher drain hose to the underside of the sink creating a “high loop).
Under the sink, connect the dishwasher hose to the small inlet of the air gap with a hose clamp. Connect the larger outlet of the air gap to the discharge hose that you bought and the other end to the garbage disposal inlet (be sure you remove the knock-out plug from the garbage disposal first) and secure everything with hose clamps. Push the air gap into the hole in your sink or countertop and screw on the retaining nut. Then you can install the decorative cover over it. Run the dishwasher’s “rinse and drain” setting and check for proper operation.Plumbing Leak Under Sink When Dishwasher Runs » « I Have to Push Hard on My Door to Get It to Latch