Often, but not always, a host will provide phpBB and MySQL. Frequently they're out of date, however. You should check with your host as to their availability. Usually the host's own site will detail exactly what you're getting for your money.
To learn more about the applications themselves, I recommend that you visit the phpBB forums
. Be sure to take advantage of all the installation documentation, tutorials, and articles in their knowledge base - accessed via their Support tab
. Equally helpful are the MySQL forums
, which also have documentation, articles, and forum support.
Good luck with your site!