A department is one section or part of a larger group, like a company or a school. The philosophy department of a university is just one of many, including English, math, and sociology.
Your local hospital has an emergency department, as well as surgical and mental health departments, or units. A company might have finance departments and hiring departments, and a town government has public works and fire departments. A "department store" is likewise split into sections. In each case, the departments specialize in one certain aspect of the organization. You can also say, "Making cookies is my department," if you're the person in your family who's the baking expert.