Congratulations!!!
One of my friends went to Sussex University and thoroughly enjoyed it.
Yeah, unconditional means that they've given you a place with no conditions attached to it - which is basically the only type of place you can be given if you've already finished high school! Conditional offeres require the student to pass their final exams with certain grades, and since these exams haven't been taken at time of application, the acceptance is conditional on these grades. If they don't get the grades needed, the student will lose their place at the university.