Suppose you notice a typo in your repo description or you didn’t specify one at the time you created the repo. To the far right, you’ll see an edit button.
Clicking this button allows you to edit a description and a website URL.
Give it a little while, but your repo description will end up on the GitHub.com search page when you do.
I’m sitting here wondering, “is this a useful tip?” but then I remember that feeling I felt when I (finally) found how to do it. Originally I thought I had to update a repo file somewhere, since it took me a while to get used to what files GitHub’s UI gets it’s info from (e.g. license) and what files are metatdata for the GitHub repo itself.