How is /etc/motd updated?

It's updated by pam_motd on login. The update-motd manual page describes this:

   Ubuntu introduced the update-motd framework, by which  the  motd(5)  is
   dynamically assembled from a collection of scripts at login.

   Executable  scripts in /etc/update-motd.d/* are executed by pam_motd(8)
   as the root user at each login, and this information is concatenated in
   /var/run/motd.  The order of script execution is determined by the run-
   parts(8) --lsbsysinit option (basically alphabetical order, with a  few
   caveats).

   On   Ubuntu   systems,  /etc/motd  is  typically  a  symbolic  link  to
   /var/run/motd.

The accepted answer above is correct, however incomplete. I'm hoping this provides a bit more info for the OP.

Basically, on a fresh install, the motd is generated from three places:

1. The scripts in /etc/update-motd.d/
2. The compiled binaries controlled by /etc/pam.d/login
3. The /etc/legal file

Number 3 there refers to the block of text at the end of your motd that includes "Ubuntu comes with ABSOLUTELY NO WARRANTY ...", that's the /etc/legal file. However you will not find anything under /etc/update-motd.d/ that mentions it, nor does the word "legal" appear anywhere in the /etc/pam.d/login file. It's inclusion has been made obscure and I really don't know how it gets in there. I mean I know there's a {$HOME}/.cache/motd.legal-displayed but I don't know where that comes from either (yet).

The /etc/pam.d/login file is responsible for the notification of pending email, however that is not obscure. There's a nice comment describing:

Prints the status of the user's mailbox upon successful login

...right there in the file. I suppose technically that is not really a part of the motd, but it shows up at login and if you're new that fine distinction may not be appreciated.

On a fresh install of 14.04 there is no /etc/motd file. If you create one (or create a motd.static and symlink it to motd) the contents of that file will be appended to text generated by the update-motd.d scripts but the contents of /etc/legal will stop showing up. Go figure. The email notice still appears so this does not interrupt the /etc/pam.d/login script so I doubt /etc/legal is being pulled in from there. Its sourcing remains a mystery for the reader. I have noticed that when I remove the /etc/motd link (or file) the legal disclaimer does not immediately come back. It takes a few minutes. I did not want to constantly see the disclaimer so I deleted the text from that file.

Cheers.

To expand a little on David Kuhl's answer:

A fresh install of Ubuntu Server 14.04.1 LTS apparently does not install landscape-common nor update-notifier-common packages. Thus the following scripts are not installed:

/etc/update-motd.d/50-landscape-sysinfo
/etc/update-motd.d/90-updates-available

Thus, to get all of the ssh login information available from servers migrated from 12.04 LTS one must install the above packages manually:

sudo apt-get install landscape-common update-notifier-common