Unique means unique. Only one, not many.
For example:
(1) A point outside the straight line, with one and only one straight line perpendicular to the known straight line;
It means that beyond the straight line, there must be a straight line perpendicular to the known straight line, and there is only one, and there will be no second one.
(2) At a point other than a straight line, one and only one straight line is parallel to the known straight line.
It means that at a point outside the straight line, there must be a straight line parallel to the known straight line, and there is only one, and there will be no second one.