Readable addresses help both customers and search engines, and CubeCart can produce them.
Turning them on
Enable search engine friendly URLs in the store settings. CubeCart needs the rewrite rules in .htaccess to be present; if they are missing, every page except the home page returns 404 – the same symptom as the WordPress permalink problem, and the same cause.
If everything 404s afterwards
Check that .htaccess exists in the store root and contains CubeCart's rewrite block, and that the file is readable at 644. If you turned the setting on and the site broke, turn it off, restore the site, then sort out .htaccess before trying again.
Changing URLs on an established shop
This is the part that needs care. If your shop has been indexed with one URL format and you change it, every indexed address changes at once. Without redirects you lose that traffic, and it can take months to recover.
Plan redirects from the old format to the new before switching, and expect a temporary dip while search engines catch up.
Keep them stable
Once live, treat product and category addresses as permanent. Renaming a category changes the addresses of everything in it. If you must, redirect the old ones.
One address per page
Make sure a product is reachable at one address, not several. Duplicate addresses for the same product split its ranking. Canonical tags help, but a single clean address is better.