To move items you must have Browse + Access + Modify permissions for both the source folder and the destination folder. If you want to move a folder, you must also have Browse + Access + Modify permissions for the entire underlying folder structure of the source folder.
To move an item:
Select the items or folders to move.
Comment: You can multi-select using Ctrl or Shift.
Click the Move icon.
Response: The Select Destination Folder dialog appears.
Select a destination folder.
Click OK.
Select how you want to handle any potential name conflicts, and click OK.
Comment: Read more about how to handle conflicts in How Are Conflicts Resolved?
The moved folders will keep any permissions explicitly set for them. If a folder is set to inherit its permissions, then it will inherit its permissions from the new parent folder after it has been moved.
See also: