Yes, last visit means that they visited. It does not, however, mean that they made it past the screen pictured above. I know, it is confusing, but truly, the last visit counter counts any page served as indicative of a visit, and in this case it is the closed message that they are being served.
When you block a person, they can no longer invite you to a private message or post to your profile wall. Replies and comments they make will be collapsed/hidden by default. Finally, you'll never receive email notifications about content they create or likes they designate for your content.
Note: if you proceed, you will no longer be following .