Only the Company Owner or Admins can change a user's department.
To change a user's department, go to the Directory tab. 
Find the user you wish to change his or her department within the Directory tab. Then, click "Actions" to the far right hand side from the user's name. 
Then, click on "Edit User". 
A Edit User window will appear. Click on the Department field underneath the Start Date. 
Click on the new department name within the drop down window. 
Click "Save User". 