How to see the details which Ubuntu shows at the time of login anytime?

Looks like it changed. With Ubuntu 16.04 there is no /etc/motd but you can cat /var/run/motd.dynamic instead.

You can show anytime when you wish this message - message of the day - using next command in terminal:

cat /etc/motd

or, better:

for i in /etc/update-motd.d/*; do if [ "$i" != "/etc/update-motd.d/98-fsck-at-reboot" ]; then $i; fi; done

If you want to see this message everytime when you open a terminal, just insert one of the above lines at the end of ~/.bashrc file (you can open it with gedit ~/.bashrc command).

The /etc/motd is a file on Unix-like systems that contains a "message of the day", used to send a common message to all users, in a more efficient manner than sending them all an e-mail message.

More about: http://en.wikipedia.org/wiki/Motd_(Unix)

Related: How is /etc/motd updated?

Ubuntu runs this at login:

/usr/bin/landscape-sysinfo

You can simply run it through terminal using following command:

landscape-sysinfo