A strange name, having nothing to do with the actual trick. It derives perhaps from the fact that when the trick was first performed, it was assumed that the assistant would always be a lady, one who appeared to want to admire herself in the mirror.
A large mirror in an elaborate frame is brought on to the stage. It's perhaps five feet wide by eight feet in height. The bottom of the mirror is a couple of feet off the ground, allowing the audience to see that there's nothing under it or behind it. Curtains extend to either side for a couple of feet. There is a bar across the mirror, a foot or so above its bottom; at the top of the mirror is a panel extending upwards a couple of feet. Brackets are placed at the height of the bar, one on each side of the frame.
A bar and a sheet of plexiglass are brought on. The bar is placed on the two brackets and the plexiglass on it and the bar across the mirror. The assistant steps onto the plexiglass and immediately turns her (let's go with a lady) back to the audience so as to look at herself in the mirror. The performer attempts to get her to turn around a couple of times, but gives up. A screen in the form of a three-sided box, not as wide as the mirror but tall enough to reach to the top screen, is brought on. It's placed behind the lady on the plexiglass shelf for a few seconds, then withdrawn. She's gone!
The mirror is actually double. The one in front has a small rectangular cutout at the bottom, large enough for the lady to wriggle out through, on her back. The back mirror is moveable, sliding up and down like a window. It's the same height as the front mirror. When the screen is applied, the backstage people raise the back mirror (aided by counterweights if necessary), the lady goes out and along a ramp through a hole in the back set, which is immediately concealed.
As soon as the screen is placed on the shelf, the assistant must start to sink down and get out, just as the assistants must immediately start to raise the back mirror and extend the ramp that she uses. An exceptionally flexible assistant might be able to get out while facing the audience but then the point of having the mirror is lost. Of course enormous care must be taken to ensure that the edges of the cutout in the front mirror are imperceptible. It's seen that the panel at the top of the frame conceals the raising and lowering of the back mirror. The fact that the concealing screen is not as wide as the mirror adds to the mystification.