At the bottom of each post is a gray box that shows the tags, categories, and Leave a Comment as well as a chance to Edit this Post.

Not sure if this is a plug-in or part of wordpress but I don't want people to have the chance to edit a post, so how do I disable this?

the edit this post only shows up if you are logged in and have a high enough wordpress user authority to edit posts. Logout and look at your site again

Got it, thanks for helping.