Also...look up in the upper righthand corner of the screen - see the little red oblong with a number? Hover over that, and you'll see Alerts and Private Messages. Anytime that turns red, you've got one of those two things...
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 .