It appears that it does not really have a well-defined purpose. According to the docs:
Creating a database cluster consists of creating the directories in which the database data will live, generating the shared catalog tables (tables that belong to the whole cluster rather than to any particular database), and creating the "template1" and "postgres" databases.
[...]
The postgres database is a default database meant for use by users, utilities and third party applications.
There is also the database template0, your safety net when you screw up all others.
postgres is your default database to
connect with.
template1 is your default for
creating new databases, these are
created just like template1
template0 is usefull when template1
is corrupted (wrong settings etc.)
and you don't want to spend a lot of
time to fix this. Just drop
template1 and create a new template1
using the database template0.
When a client application connects to a Postgres server, it must specify which database that it wants to connect to. If you don't know the name of a database (within the cluster serviced by the postmaster to which you connect), you can find a list of database names with the command:
psql -l
When you run that command, psql connects to the server and queries pg_database for a list of database names. However, since psql is a Postgres client application, it can't connect to the server without knowing the name of at least one database: Catch-22. So, psql is hard-coded to connect to a database named "postgres" when you run psql -l, but you can specify a template database in that case:
After initialization, a database cluster will contain a database named postgres, which is meant as a default database for use by utilities, users and third party applications. The database server itself does not require the postgres database to exist, but many external utility programs assume it exists.
[Note: A database cluster is a collection of databases that is managed by a single instance of a running database server.]