Here you will be asked a series of questions.
Database Server Hostname : usually leaving this as localhost works, but not always. If not, you can usually find this information from your hosting control panel, but if you don't see it, contact your hosting company and they can tell you. If you get Critical Error: Could not connect to database - then localhost probably didn't work.
Your Database Name: This is the name of the MySQL database you wish to store the phpBB information in. This must already exist.
Database Username: Your MySQL database login username
Database Password: Your MySQL database login password
Prefix for tables in database: Unless you are using a single database to hold more than one phpBB, you probably don't have a reason to change this, so leave it as phpbb_