If all of the scripts and applications you run that need MySQL are running locally (on your computer) then they will refer to the MySQL server as either "127.0.0.1" or "localhost" with a ":/tmp/mysql2.sock" or ":3306" tagged on the end; You can mix and match all four, it's all the same.
If however you have people outside your computer that need access to your database, you'll need to get a dynamic DNS client (like www.no-ip.com which I find works great on OS X).