When you complete a puzzle, you will be prompted to send a message to the person you got it from.
This assumes that the website knows who you got it from.
When you fill in the completed date for a puzzle, of the website knows who you got that puzzle from, you will be prompted to send a message. It is a simple YES or NO prompt (or NEVER if you want to switch the feature off).
The message simply lets the other person know you completed the puzzle and attaches a stock picture. The message is sent in the normal chat area so you can add more comments later or even a picture of the finished puzzle. But the automated message is rather simple. This is to help promote the social side of puzzling.
If you turn off this feature, you can always turn it back on by clicking on the menu icon in the top/right corner of any screen,selecting the 'settings', then 'account settings' and finally 'change other values' options.
Hopefully, this will make trading puzzles more fun and social.