Tagging someone in a post is just directing a comment to a specific person and then that person is notified of said comment so that they can go to the post and read it. It adds to the conversation aspect that a lot of forum posts take on.
An example... I recently came across an older forum thread in which a member posted a picture that I liked very much and in my reply I wanted to pay my compliments to that member. Because that thread is on the older side, that member may not be following the thread anymore and my comment would not reach its intended audience. A tag would notify the member that they were mentioned in the post so that they could click over to the post and see the reply and my compliments.
I'm sure a lot of people have come across an instance where they wanted to direct a "Rick, I love what you did with your garden but you need more compost!" within a multiple page thread. Typing
@RickCorey (or whatever process is set up) tags Rick in the post and he would get a nice link to the post on his homepage so he could receive all the accolades he is due.
