This feature lets you verify that you own the website on your Pinterest profile.
When your website is verified, people will see a checkmark next to your domain in search results. They will also see the full website URL and checkmark on your profile. Confirming that you own your website adds your profile picture to any Pin that came from your site. You’ll also get access to website analytics so you can see what people are saving from your website.
For information on how to verify your website, visit this Support article.