Why is there an edit hyperlink?

Hope that helps. The reason there is an Edit Links hyperlink there is because you have the permission to do so, most likely by have the Design permission. If your users do not have that permission level access, they will not see the link.
For More Information Please Refer:
https://sharepoint.stackexchange.com/questions/65162/how-to-get-rid-of-the-edit-links-link-in-the-top-navigation-sharepoint-2013
You May Also Like to Read: