From the figure, its clear that the compass drew arcs like below:
With A as centre, and more than half of the length of AB as radius, one arc is drawn.
With the same radius, with B as centre, another arc is drawn.
The points of intersections of the arcs are X and Y.
Clearly, this is the construction of a perpendicular bisector of the line segment AB.
Hence, if we draw a line segment through XY, it will be a perpendicular bisector of AB.
