Departments group practitioners for the team view, reports and the booking page. They're labels, not permissions, and have no effect on scheduling.
What a department is for
A department is a label on a practitioner: Physiotherapy, Massage, Podiatry. It groups the team in the Department hierarchy view, is a filter on reports, and sorts practitioners on the booking site. It has no scheduling impact; availability, locations and appointment types are set separately.
Set it
Open the practitioner under Settings, then Users & Practitioners, and under Practitioner configuration find Department. Pick an existing name or type a new one; the list grows as you use it. Save.
See the whole team
Select View hierarchy on the Users & Practitioners page to see practitioners grouped by department, with anyone not yet in one listed last under No department. To rename a department, change it once under Settings, then Autocomplete Labels, in the Departments list; every practitioner in it follows.