There are numerous ways to export a group of pictures selected in Shotwell.
The file pane at the left hand side of the application window is a virtual library with a directory structure and folder names that do not map directly to the system's file directories. This can throw you off if you're coming from windows because the photo managers I've used there display a file directory identical to the system file directory, so you can drag and drop pictures to move the files around.
With Shotwell it's a bit more involved; Here's how to do it:
First create the group of pictures you wish to move about your file system -- here is a short, screenshot-laden tutorial for two ways of doing that: http://www.linuceum.com/Desktop/Shotwell.php -- but to make things flow, I'll add a method not mentioned in the linked tutorial: flags.
Navigate through your Shotwell directories, and flag the photos you want to include in the group of pictures you wish to move. Do this by right clicking the thumbnail, and selecting 'flag' from the right-click menu.
In the file pane towards the top you will see a directory named "flagged." Click on that directory, and all the photos you've flagged will display in the viewing pane. Select all the photos--control A--and click on the 'file' menu at the top of left of the screen. Select Export...and a dialog will pop up, which ends with the file manager's file choosing screen, where you can choose or create the directory to where you wish to move the selected photos. That's it.
I should note that you aren't actually moving the photos. You are but creating copies of them.