What the heck are these L-shaped screws and how do I use them to hang my vanity mirror
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.