SQLite is a smart library that implements an embeddable SQL database engine. No need for an external database server - an application linked against libsqlite can do it all by itself. Of course there are a few limitations of this approach compared to "real" SQL database servers, mostly for massively parallel high-throughput database applications, but on the other hand, installation and administration are a breeze. Your application should support the sqlite driver if one of the following applies:
You want to support potential users of your application who don't have the skills to administer a database server.
You want to offer the simplest possible installation of your application.
You want to let users test-drive your application without the need to fiddle with their production database servers.