FogBugz lets you group projects by client, which is helpful when you work with multiple clients, each of which may have multiple projects. You can also group projects by department, which is helpful when your team is divided into different departments, each of which may work on multiple projects.
Clients and departments are really the same thing: a way to group projects, and assign permissions to people to access those projects.
To group projects by client, log on as Administrator and go to Settings | Clients. Set up your clients. Then edit each project in turn, assigning it to the appropriate client.
To group projects by department, log on as Administrator and go to Settings | Departments. Set up your departments. Then edit each project in turn, assigning it to the appropriate department.
Each project can be assigned to exactly one client or one department, but not both.
There are two reasons to group projects by client or department: