To move data:
1) Select any level of the hierarchy tree
2) Either use the "Move Files" icon from the ribbon or right-click and select "Move Files" from the new pop-up menu
3) When the "Destination Directory for File Move" window appears, use the "Browse" icon 
4) Click the "OK" button and the move will begin
NOTE - Make sure that there is enough room in the destination location to prevent any potential errors or data loss
See the attached video for a sample of the Move operation.
Related Articles:
What is the difference between "Move" and "Import/Export" when using Motion Explorer?
How do I "Export" then "Import" files using Motion Explorer?