Post slugs allow you to create the "link" displayed in the browser and only comes into play when you use pretty permalinks.
By default, WordPress will use the post title as the post slug
Example:
The post slug is 'one-click-vs-manual-wordpress-installation' (same as the title)
However, defining your own post slug allows you to customize how the link displays in the browser
Example:
The post slug is 'datafeed-user-guide' (not the post title)
Defining a custom slug can be beneficial when you have really long titles, or when using a quirky title to catch eyes.
Hope that makes sense
Regards,
~Teli