It is not mandatory to setup departments within Web TimeSheet, however if you do not setup departments within the application it effectively means that there is no organizational hierarchy that users can be associated to.
Can setup timesheet periods unique to each department.
Can define the hierarchy of the organization within the application. This helps in sorting users within the application.
While running reports, you can select the department you want to run the report for and not all of the users.
Department setup is a pre-requisite for Hierarchy Filtering. This restricts users access to the system based on their hierarchy.
Note: While not setting up departments will definitely put the administrator at a disadvantage when they need to maintain lot of employees within the application.