I wouldn't have an Object type parameter, no point in casting it to Student if we know it will always be type Student.
As for an explanation, "result == 0" will only occur when the last names are identical, at which point we compare the first names and return that value instead.
public int Compare(Object obj)
{
Student student = (Student) obj;
int result = this.getLastName().compareTo( student.getLastName() );
if ( result == 0 )
{
result = this.getFirstName().compareTo( student.getFirstName() );
}
return result;
}