Products not displaying

This option will remove the ids from the URLs as some people like to remove them (even though it doesn't help much with SEO...)
Thus, the system will only have the alias of the products/categories to rely on to find the products/categories to display when you click on a link without the ids.
And if you don't fill the alias of the products/categories, the system will use the product/category name and convert it to a URL compatible format (without special characters, spaces, etc). And in such cases, or if your product/category name starts with a number, the system won't find the corresponding product/category when you click on the link and thus you'll get such issue.
Having the ids in the URLs ensures that whatever you put for the product name/alias, it will always work.
So if you remove them, the best would be that you fill in the alias of each product/category without starting numbers, and without special characters or spaces so that the alias in the URLs would be exactly the alias in the product/category and in that case it will work fine too.
It's just easier to keep the ids in the URLs and don't bother with the aliases.