There are holes on the top left and top right corners of the mirror that look like this.
The black things are wall anchors in case you are not screwing into solid wood, but plasterboard (or holes drilled in concrete.)
The hanger holes are large because the entire end of the "L" goes into the hole, and then the mirror drops down so the "L" holds it until it's lifted up again.
Hopefully obvious that the end of "L" should point up.
Those black things help secure the screws in to drywall.
Drill a hole the size of the black thing into your wall and tap it in to the hole in the wall. Make sure it's snug.
Screw twist the L screw into the black anchor and the black anchor expands to keep the screw in the wall.