Let me try to explain...
Ticket Assignment
Use help topics and/or ticket filters ;)
Department
All members of a department should be in here - just like the departments in your company.
Team
A team (member) can see tickets that are assigned to the team, even though the team members are all in different departments and only see the tickets in that department, so e.g. a second level agent which is a member of the department A can also have access to the tickets of department B when they are assigned to the team A&B and not to the department B or an individual member of a department B.
Group
Here you define the permissions for the agents, e.g. if they are allowed to create or delete tickets and so on. These permissions are then assigned to the agents / departments.