If I were to move host. I assume I can't just copy paste the public_html content?
Would this mean all posts are lost? Where are they stored?
What are the steps?
This tutorial should be relevant:
http://community.mybb.com/thread-27771.html
Edit:
Sorry, didn't notice that post was from 2008. Things have changed a bit.
Try this (Should be easier to do):
Take a dump of the database on the old webhost (Use PhpMyAdmin).
then create a new database on the new host, and import this dump.
Then copy your stuff from public_html to the new host.
Edit the ./inc/config.php file to connect to the new database