This is a little complicated, but here goes…
Video images have what is called an “aspect ratio”, which is the ratio of how tall something is by how wide it is. Standard televisions have a 4:3 aspect ratio, which means for every three units that the television is tall, it is four units wide. It looks like a square but it is slightly wider than tall.
But a theatrical film, at least those made since circa 1956, is typically much wider than 4:3. To fit the widescreen image onto the square screen requires that you either fit the movie’s top and bottom to the screen’s top and bottom, cropping off the sides—what’s called “Full Screen” or “Pan and Scan”—or you scale the image down so that the entire image fits, side-to-side, which means a lot of empty space at the top and bottom of the screen—“Wide Screen” or “Letterbox”.
But DVDs have a fixed vertical resolution—480 pixels tall. So scaling down a movie to fit the screen means you’re throwing away up to half the potential vertical resolution of the image. Since the advent of widescreen and HD televisions, this loss of detail has become unacceptable to viewers. So instead of squashing the movie vertically, most DVDs made in the last five years are “anamorphic” transfers that squash the movie horizontally.
They take the DVD image, fit it to a 16:9 aspect ratio (wider than a standard television, and the proper width:height ratio for a widescreen or HDTV) and then squeeze the sides in to fit the entire image in a 4:3 aspect ratio. The human eye is much better at resolving vertical resolution than horizontal, so what you get is an image that has twice the detail by using the entire available vertical resolution, and the softening along the horizontal is negligible.
When played back in a DVD player, the player automatically fixes the image to fit your screen. If attached to a widescreen TV, HDTV, or widescreen computer monitor, the DVD player knows to stretch the film sideways to fill the entire screen. If attached to a standard “square” television, the DVD instead squashes it vertically, on the fly, to fit it into the screen. On a standard television, the effect is essentially the same as a 4:3 letterboxed DVD; it is on the higher-resolution screens that the anamorphic transfer makes the difference.
The reason you are seeing double black bars is this: many movies are in fact wider than 16:9—which can also be written as approximately 1.77:1. Movies frequently go as wide as 2.35:1, which means that even given the larger canvas of the 16:9 anamorphic transfer, there are still black bars along the top and bottom of the image. DVDs cannot compress black as “true black”, but instead tend to be a slightly lighter blackish-grey.
When playing a DVD on a 16:9 monitor, with the DVD image filling the screen, you won’t notice. But when you play it on a regular TV, your DVD player is shrinking the film vertically to fit your screen. That means that there is a portion of the screen that is not being used at all, and is completely dark, above and below the 16:9 frame. Then there are the not-quite-black bars, which are embedded in the 16:9 frame, which are clearly visible because you can compare them to the true black surrounding them, then there is the movie itself.
That is why you see “double bars”.