A database is basically a collection of tables and each table is a collection of data organized and sorted however you design it. Chances are that you want to only create one database with lots of different tables to store your information. For simple web applications (or most simple applications) you will only need to set up one database. There are times when multiple databases are better or required, but it depends on the situation.
If you need help designing your database, check out the SQL forum.
(Oh, and to answer your question, there is no such thing as a sub-database.)