Association is a basic and loose form of relationship; two objects know about each other, but are not strictly dependent.
Aggregation is a special case of association; objects represent a 'has-a' relationship, where one object contains a reference to another.
Association and aggregation allow objects to exist independently of each other.
In the context of a Student-University relationship, association allows for change of universities, while aggregation, in the case of departments and professors, allows for the existence of professors even if a department is removed.