All websites should be protected with HTTPS, even ones that don't handle sensitive data. HTTPS prevents intruders from tampering with or passively listening in on the communications between your site and your users.
HTTPS is also a prerequisite for many new, powerful web platform features, such as taking pictures or recording audio.
By definition, an app cannot qualify as a progressive web app if it does not run on HTTPS. This is because many core progressive web app technologies, such as service workers, require HTTPS.
For more information on why all sites should be protected with HTTPS, see Why You Should Always Use HTTPS.
Migrate your site to HTTPS.
If you're running your own servers and need a cheap and easy way to generate certificates, check out Let's Encrypt. For more help on enabling HTTPS on your servers, see the following set of docs: Encrypting data in transit.
If your page is already running on HTTPS but you're failing this audit, then you may have problems with mixed content. Mixed content is when a secure site requests an unprotected (HTTP) resource. Check out the following doc on the Chrome DevTools Security panel to learn how to debug these situations: Understand security issues.
Lighthouse waits for an event from the Chrome Debugger Protocol indicating that the page is running on a secure connection. If the event is not heard within 10 seconds, the audit fails.