A database is a place to store data. Data can be anything from a last name, to the date someone last visited your site. If you want to store information to be used in your business (e.g. customer mailing lists) or on your website (e.g. a product catalog), you're going to need to use a database.
A database's complexity depends on the way the data will be used. When you work with us you don't need to worry about the details of your database. That's something we're happy (yes, really) to figure out for you.