PostgreSQL is a free and open-source relational database that can be deployed as a plugin on Railway. To backup a Postgres database on Railway, users need to install the psql client and use the `pg_dump` command, which writes a file locally with a copy of the database. The command requires information from the Project Variables page, such as the username, host name, port, database name, and password. Once the command is executed, the backup can be restored using the `pg_restore` command, which connects to a PostgreSQL database and restores a backup made from `pg_dump`. The restoration process also requires information from the Project Variables page. With these steps, users can create backups and restore their Postgres databases on Railway.