This is what's called a "captcha" code. http://en.wikipedia.org/wiki/CAPTCHA
It's a device to foil spam robots. It's there to tell that you're human and can read the code (which is often difficult, even for a human to read).
Since you're anonymous -- not a logged-in WikiTree member -- you have to enter one there and you had to enter one to post your message here.
The code is uniquely generated every time.
On the private message form we also have a second back-up anti-spam device because the captcha wasn't enough. This just asks for the first letters of the alphabet, i.e. ABC.