The quick connect fitting is used in a variety of applications. Anywhere you're connecting a waterline or air pneumatic lines you will see a compression fitting used. If you're just hooking up drinking water systems, you're probably going to use a quick-connect or a quick-disconnect type fitting.
The angle-stop underneath your sink is an example of a compression thread. These types of flex lines often will use compression type threads to hook up to a coffee brewer, for example. Some have a faucet connection on one side and then the angle-stop connection, which is your compression thread, on the other. You can use just a regular compression nut and sleeve to attach tubing to the top of an angle-stop. These fittings all connect the same way.