After I have installed Ubuntu server I was asked to enter my user name and password so I can login after the installation is done. But I was not prompted to enter root password. By default, root can’t login to terminal in Ubuntu. 

But you can do administrative tasks like install of new software, configuration using the sudo command. But if you intend to do administrative work only it’s not fun to type sudo before each command. 

One way how to avoid this is to use sudo to go into permanent root mode in terminal (start /bin/bash as a root shell so that you can enter a root user command without using sudo command).

sudo -i

But if you really want to be able to login as user, you need to create it’s initial password by login into terminal as yourself (using the credentials entered during insatallation) and typing

sudo passwd

You will be prompted for your current password and subsequently for the new root password (and once more for retyping it).

After that is done you can login to terminal using root account and the just created password