PostgreSQL is an extensible database. I hope you've learned this much by now. It is extensible by virtue of the design that it has. As discussed before, PostgreSQL uses a catalog-driven design. In fact, PostgreSQL is more catalog-driven than most of the traditional relational databases. The key benefit here is that the catalogs can be changed or added to, in order to modify or extend the database functionality. PostgreSQL also supports dynamic loading, that is, a user-written code can be provided as a shared library, and PostgreSQL will load it as required.
Extensibility is critical for many businesses, which have needs that are specific to that business or industry. Sometimes, the tools provided by the traditional database systems do not fulfill those needs. People in those businesses know best how to solve their particular problems, but they are not experts in database internals. It is often not possible for them to cook up their own database...