A database (or DB) is any structured storage of data. In XOOPS terms, it means a database that contains (or will contain) both the information needed for running your XOOPS site and your content.

XOOPS uses a SQL-based RDBMS to store information. Currently only MySQL is supported as the database server, and although the object oriented nature of XOOPS makes it easier to add support for other engines no official version has implemented it. It has been reported that changes in the way DB schemas (structure) are created will arrive for the next major version and make XOOPS cross-RDBMS for production.

Your server/hosting service must have a MySQL server running and you need to provide a username, password and server address (usually localhost: the IP of the database server can be the same of the HTTP server) for XOOPS to install and work correctly. This information must be kept safe, since it would allow anyone to alter your DB (even erasing it).

Usually hosting companies make DB management tools available. The most common for MySQL problably is phpMyAdmin and you can use it or a similar tool to access/modify/input raw data into your MySQL database.

See also this FAQ here