Something that's unassigned hasn't yet been distributed or matched up with anything else. If your train ticket doesn't list a particular seat, then the seats are unassigned and you can sit wherever you like.
When you start a class, you’re usually given a syllabus listing assignments for at least the first few weeks. Readings for later in the semester may be unassigned, so the instructor can determine students' interests and make assignments accordingly. If you've just changed your hair, gotten new glasses, and become a stand-up comedian, you may want to change your email address to reflect the new you. If the address you want is unassigned, you shouldn't have any trouble getting it.