HTTP Nowhere upgrades non-secure web connections to secure: it upgrades HTTP URLs to HTTPS.
If the web site does not correctly support HTTPS, Chrome will refuse to connect (with the usual interstitial warning page). Thus, this extension will make it hard to view some web sites.
For maximum safety, you should also turn on Chrome’s Secure DNS (DNS over HTTPS) feature. There is no way (yet?) for an extension to turn this on for you, so you have to do it manually. To do so, go to the dots menu → Settings → Security, and then scroll down to Use Secure DNS. Select a provider or fill in your own. (You can also get to this setting by navigating to the URL chrome://settings/security?search=dns.)
HTTP Nowhere is designed to be as simple as possible, and has no functionality other than upgrading connections. This is easy to see in the very short and simple implementation.
It needs no special permissions or access to the web pages you view. There is nothing to configure; HTTP Nowhere is either on or off.