Departments are a great way of giving an indication of where various members of staff fall in relation to your company. They give you extra power to run searchs against data helds against specific departments as well as giving Department Administrators the ability to reset passwords for the users under them.
They are easily managed from Admin > Organisation > Departments before hitting New on the right hand navigation panel. When creating a new Department, you need only provide the name and any Administrators you wish to assign to it.
Once you have created the Department, click into it and hit Manage Members on the right hand side to open up a contact selector and add any members you wish to add before hitting OK.