I had a question on LCDs after noticing something interesting about its color. LCDs are black when they aren't used. But when we observe LCDs closely, we see they are made up of red, green, and blue dots. Therefore, since they reflect red, green, and blue, collectively, an LCD screen should look white. So why does it look black?
The vast majority of color LCD screens are transmissive in design. This means they require a backlight to provide (generally white) light that is then allowed to pass through the pixels on the screen. These pixels are turned from transmissive (i.e. clear) to opaque (i.e. dark) in order to create the display you see. Each pixel can be made to appear a specific color but instead of reflecting the color, as you said, the light is actually filtered by a colored section of the pixel. The pixels each have three sections, and each section can transmit one of the three colors. To make a pixel look red, the red section turns to transmit the backlight while the blue and green sections stay dark; resulting in only red light coming through.
The LCD screen is black when it is off simply because the backlight is also off. Try it at home: turn the brightness all the way down on your laptop or LCD desktop monitor. Then shine a flashlight at it. You should still be able to see the graphics, but the colors will not be as clear since now you are actually looking at reflected light instead of transmitted light.