Story Links are tracked links to evaluate how many people Swipe-Up in your Instagram Stories.
They can only be used by Instagram accounts with more than 10,000 followers and the Swipe-Up feature.
How to use Story Links
Open the Instagram app, then On the Story creation page, at the top, you should have a Link icon, where you can add a website. You can add the swipe-up link there.
See screenshot below, the icon is highlighted