Backing up WP – don’t understand the MySQL

I’ve always pretended that the stuff behind WP is magic – I put tags into my HTML and, voil??, it all works. But now I need to move my website, and WP doesn’t create the cute little .html files that MT used to that made it very easy for me to transport my blog entries.
How do I export my blog entries? What does the MySQL db have to do with it?
Thanks for any help.