HTTPS is the secure form of HTTP, the protocol a browser and a website use to exchange data. Traffic is encrypted with a TLS certificate on the server. That stops anyone along the way from reading what a visitor enters, such as an address in an order form, and from altering the page in transit. You recognise it by https:// in the address bar.
Why does it matter?
Google lists secure delivery of pages as part of page experience, and Search Console has a report showing whether your pages are served over HTTPS. For visitors it is mostly about trust: a form on an insecure page puts people off.
Example
A site moving from http://www.example.com to https://www.example.com technically changes address. Google treats that as a site move with URL changes: every http URL gets a 301 redirect to its https version. You do not need to submit a change of address in Search Console for this.
Common mistake
Having a certificate while the http version stays reachable without a redirect. Two versions of every page then exist; Google names http and https as a known cause of duplicate content. A second mistake: internal links, canonicals and the sitemap that still point to http://.
What else to arrange when your address changes is covered in Redesigning your website without losing search visibility.