What do we mean by a 'Data Base'.
A database is a collection of tables. A table is similar to an Excel file. A database contains several of these tables. If you have used Access then you are familiar with a database.
Databases are fun to create. That is probably the nerdiest thing anyone would ever say, but it is true.
A databse would be necessary if you wanted a guest book, a blog, or an ecommerce site.
For small web sites, databases are usually created in either Acess or MySQL. There are many other database systems out there varying in cost and scalability.
Databases interact with your web site through a scripting language such as ASP, PHP or Perl.
I generally think most small business don't need databases for their web sites. There are many exceptions to this of course. Be prepared to pay much more if you do need this additional work done.