If I use a test-script to test that all the links on a page return a status code of 200, that is an example of Automated Testing.
I might run the test-script when I start work in the morning.
I can take the concept a bit further with a watcher script which waits for me to change the app-software.
When the watcher script detects a change it could run the test-script.
Another way to enhance the concept is to use a scheduler to run the test-script every ten minutes.
This might be useful for an app which offers behavior dependent on data which is constantly changing.
An app which forecasts the stock market or the weather exhibits behavior dependent on data.
Obviously, the purpose of Automated Testing is to prevent bugs creeping into the app.
Also after the app has been deployed, I use Automated Testing to alert me when the app malfunctions due to events outside the app.