If you face this issue on your server means you need to check the status of your database server and logs to resolve this issue asap.
In My Case, I found I did not initialize the database that is why I got this error postgresql.service is failed.
So to solve this, You need to initialize the postgresql server first then start the service.
Step 1 : To initialize the database command is
Postgresql-setup initdb # postgresql Version 9.x
Another Command is
service postgresql initdb # Redhat Version 6.x
Step 2 : Now try to start postgresql server
Systemctl start postgresql