Making a Smart Mirror
Yes, a two-way mirror works the way you explained.

In more detail, a mirror is a thin sheet of a reflective metal.  This is usually supported by being attached to a piece of glass (and often protected by being covered on the back), but the actual mirror is the metal layer.  

A two-way mirror reflects some proportion of the light, and lets the remainder through.  If it is placed between a brightly lit room and a dark room, it looks transparent in the dark room (showing the light room), and reflective in the light room (also showing the light room).

If you put a two-way mirror over a display, the mirror will look reflective when the display is off, but show the the display (if it is bright enough) when it is on.