On Linux its common to log into a system via SSH or serial console. There is a standard message that welcomes every user. It can be changed, which is handy to pass on any introductory information to new users or to identify the system on logon.
The text you receive after login via shell comes from the file motd in /etc. So, in order to greet your users, or yourself, in a custom way, you have to edit this file: /etc/motd.
But note that on Debian, this file is just a sylink to /var/run/motd, and this file is overwritten on each startup.
There are a number of tricks to prevent that or reinstate your custom message. But on a server system, reboots should be sufficiently rare so that manually the file isn't such a big deal.
Banner (prior to login)
In case you need to show some info to users before they log in, for example to satisfy legal constraints, warn users, or just tell them something important before they log in, SSH protocol version 2 offers the Banner scheme to send some text to console prior to login. Here's how to do this. Basically, you reference a file from the sshd config with the signature/message to display.
Fancy ASCII art
To end this post, it's probably a good occasion to suggest adding a bit of ascii art to round things off in a nerdy way.