Links to products on your site are automatically generated based on the name you give each product. For example, a link to a product page for apples might be http://mysite.weebly.com/store/p1/Apples.html. Product permalinks allow you to customize this link, which is handy for items with longer names - your product will keep its original name, but the actual page URL can be something much shorter.
To set a permalink, go to Store > Products and click on a product to edit. Expand the Advanced Options section and you'll see the Permalink option.
You can enter any combination of letters and numbers that you want, but you can't use special characters or spaces in the permalink. Either hyphens or underscores (or both, if you wish) can be used to indicate spaces between words. For example, you can enter something like my-shorter-name_2, but things like my shorter name and my_shorter-name! won't work and you'll see an error when trying to save.
That's it! Save the changes when you're done and check out your new custom URL on your live site.