Your department (also called a school in some faculties) is the area your course sits in, for example if you study Fine Art your department is Art, if you study Forensic Chemistry yours is the School of Science and the Environment.
The department of the year is one that has excelled in all areas of learning and support. Do you know where you need to go for support and advice? Are events and classes well-advertised? Do they put on extra sessions that are really helpful? If your department is friendly and welcoming, well organised and focused on the student experience, you should nominate them for this award.