Contraption for hanging a mirror
This is a part of a security hanger set:



Security Hanger Set

Two of the straps you have pictured go on the top of the mirror, and the clips on the right side of the picture go on the wall and hook into the straps.

One strap is installed in the bottom center of the mirror and the T-shaped screw in the center of the picture gets installed in the wall horizontally.  The mirror is hung and the T screw fits perfectly in the horizontal slot of the strap.  Then the wrench at the bottom of the picture is used to rotate the T-screw vertically to lock it into the strap.

If you only have one on the bottom of the mirror, chances are something else was used along the sides or top to hang it and the bottom strap was used only for the security T-screw.  Or the straps at the top were removed by someone to be used on another hanging.