The release notes prominently tell us that GNUmed 1.4.x requires at least PostgreSQL 9.1.
If you are running the Windows packages and have let GNUmed install PostgreSQL for you you are good to go since it comes with PostgreSQL 9.2 already.
If you are on Ubuntu or Debian Chances are your system still has PostgreSQL 8.x installed.
First check if you run any software that requires you to continue using PostgreSQL 8.x. If so you can install PG 9.1 side by side with it. If not let PG 9.1 replace PG 8.x
It usually works like this.
sudo apt-get install postgresql-9.1
sudo pg_upgradecluster 8.4 main
Then if you don't need PG 8.4 anymore you could
sudo pg_dropcluster --stop 8.4 main
sudo apt-get purge postgresql-8.4