Cypress is an integration testing tool for websites. You use it to control the browser and then test that things are as you think they should be. Visit this URL, type this, click here, find this element, test for this text, see if the URL changed, etc. We use it here at CodePen to test CodePen itself!
You can also use it to test a Pen! Gleb Bahmutov blogged about this over on the Cypress blog a little while back.
There is a little hoop-jumping in there to get access to testing inside the iframe that CodePen uses to show a preview of your code. That should still work, but it's even easier if you Go PRO and then use the Debug Mode URL to test.