phpBB2 requires a database server to store its data. MySQL is a popular database server. For example. it powers the majority of TechIMO operations.
If you do not have access to an SQL server (ask your host!), then you will probably need a flat-file forum that does not require a database.
Still, other database options are available from some hosts. Such as Access for most Windows hosts. You will need to check your host's specifications for your account.
Robert Richmond