I'm planning to use NGINX rather than Apache as my webserver on my next Magento project and am wondering about the Use Web Server (Apache) Rewrites on the Magento installer wizard?
To answer your questions:
1. What exactly do Web Server Rewrites do? I believe they just remove the index.php from the url? How important are they?
Correct, the remove the index.php for the URL to give you pretty URLs. Most modern websites and shops use them and I would recommend to do so.
2. Should this option be checked when using NGINX? Do Magento Web Server Rewrites work with NGINX
Yes, it's a setting that Magento uses to generate the URLs in a certain way. However, since the Apache rewrites don't work on NginX you'll need to replace the .htaccess with some NginX configuration which is located, probably, in /etc/nginx/sites-available/[domain].conf
Check out the Magento Wiki and this Github page for examples.
