If you have already published your website on a Free or monthly/annual paid subscription, all changes from now on will need to be manually "saved". To do this:
Go to the Publish page and click the blue Update website button:
This applies all the changes made since the last time the site was updated.
If you've already clicked Update website and your changes are still not appearing on the live site, you could be experiencing a caching issue.
Envato Sites runs a caching HTTP proxy server to route and cache requests for published site data. This means that if you visit your site more than once in an hour, you're likely seeing a cached ("old") version.
Most of the time this is fine! In fact, it's good: it means that when a visitor opens your website, instead of bouncing around the world to find the most up-to-date version, their browser will load information that has been cached (stored) locally. It's much faster to load a page from local servers that it is to load a page from a server on a different continent. Fast page loads = great customer experience.
To force your browser to find and load the latest version of the published page, just hard refresh. Hit Ctrl+F5 (Windows) or Command+R (Mac). You may find you need to do this several times.
You can also try opening your site in a Private or Incognito window, using a different browser or using a different device.