Delete them. Unless you're having other problems and need the logs to investigate, you won't harm the program be deleting them. In the Administrator, there is a section where you can set the logs to truncate every x days.
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 .