Databases can be slow, because they rely on disks for the storage of their data, but there are other overheads as well. However, DBs are usually a better way of storing significant data than flat files on disk. Arbitrary data can be retrieved quickly if it is indexed, much quicker than scanning a file by brute force.
Relational databases are a mature and very impressive technology. However, they only shine when used correctly, and how you go about querying them makes a massive difference to performance. DBs are so convenient that they're often overused, and are typically the bottleneck for a web application.
An unfortunately common anti-pattern is requiring a database call in order to render the homepage of a website. An example ...
