Create a new database in MySQL. On the \install\install.php form you fill out, you'll use that database name.
I'd used this link for general reference for some ideas on how to do it correctly. Instead of creating a user under "Setup phpBB's MySQL database and user", I'd used root later in the "Setup" for phpBB2 where it asked for database username.
Also, you can tell if your MySQL is working okay if you go to a command (DOS) prompt and type in "mysql -u root -p" [<--without those quotation marks] and it then asks for a password. Use the "SHOW DATABASES;" command to verify the defaults of test
show up if you like... and then use that again later after you create the database.