When your certificate expires, your site will appear in a browser like the following page, effectively breaking it for most visitors: https://expired.badssl.com/
There are a lot of hosting providers that provide HTTPS via Let's Encrypt at no additional charge. Unfortunately, HostGator is not one of them - according to this page, they charge between $10 and $25 per certificate installation (which would be every 3 months).
You can find a list of hosting providers that support Let's Encrypt here: