Simple Mentions works by mentioning a user in a post by typing an "@" symbol in the posting field. After entering one letter of the users name, a dropdown list of names will appear. Choose the user you're mentioning and the proper BBCode will be inserted. After submitting, the it will create a notification to that user with a link to the post.
Example: using the @ and then hit "h" will allow you to choose Hypatia, which changes into the follow bbcode: