PostgreSQL is a widely used open-source database. Since PostgreSQL is completely open source (covered by the BSD license) and does not have a separate commercial license, some people may prefer to use it. Web scripts may support the use of PostgreSQL databases, but you should first check with the developer to see if there is PostgreSQL support. cPanel does support use of PostgreSQL, but at this time, support is not as robust as it is for MySQL.
You can learn more about PostgreSQL fromhttp://www.postgresql.org/.