Departments are just for sorting people. You have, say, and English department, and all of the English faculty will have their offices in the same place. The folks majoring in English might also have some space in the department's office area, like a club room, and graduate students might have mailboxes and offices of their own in the same area as the other department faculty.
Generally speaking, you're not going to be strictly confined to one department, not even in grad school. As an undergrad you're pretty much required to take courses on a wide variety of topics and therefore from a wide variety of department. As a grad student you take more from your department, but since other departments often offer courses relevant to your field of study you can take courses from them too.
