As you've probably noticed, films come in different aspect ratios (width versus height). Most modern films are generally a wide format (around 2:1), but most TVs aren't wide format (they're 4:3). So how is the difference handled? Well, there's a variety of different ways to do it. To demonstrate the alternative image formats, I've scanned a photo in a variety of different ways:
A widescreen shot, similar to cinema screens, where the image is approximately twice as wide as it's high (actually, there's a range of different wide screen formats, but they're all around that sort of proportion).
Most cinema releases are in originally filmed with some form of widescreen aspect ratio. In other words, when you see the frame like this, you're generally seeing the entire picture.
Some common wide screen film ratios are 2.35:1 and 1.85:1 (wide screen TVs are 16:9).
The widescreen shot cropped, as if shown on TV.
When a shot is cropped, like this, you miss out on seeing the things around it. Sometimes they can be important to understanding the scene.
This is often referred to as “pan and scan”, because, usually, it's not just the centre of the picture that can be used, but the cropped section can be panned towards the side of the frame, to better show something that's not central. Sometimes you can control the position, but usually the studio has decided which portion of the whole frame that you should see.
Most programs shot specifically for TV have this ratio (4:3), which is the same as the ordinary TV picture tube (and cinema releases before widescreen came to be). Though more programs are now being filmed in a widescreen format, so they suit widescreen television sets, as they become more prevelent in the future.
The widescreen image is squashed (horizontally) to fit the entire original picture into the smaller frame (notice that the bars on the cage are no longer square). This allows the entire shot to be fitted into a normal video signal, and then later on, expanded back again to see the whole picture (incidentally, the same trick is done in the cinema, except it's done optically, not electronically).
On a wide screen set, you'd expand the frame horizontally, to fill the whole screen. Giving you a widescreen image, again.
On an ordinary TV, you'd squish the frame down vertically until the image was no longer distorted (so you could see the entire film frame, with black bars above and below it, in the letterbox format), or you could expand it vertically, so that you only see a cropped portion of the frame filling the entire TV screen.
Fitting a wide screen image into a narrow screen TV (the entire image is shrunk, until it fits the width of the normal TV screen).
Providing that your DVD player (or TV set), handles converting anamorphic images the way that you like; buying discs mastered anamorphically for 16:9 TV sets, gives you the best of both worlds. Discs mastered, this way, are often marked as 16:9 enhanced.
Some discs are mastered with the image already in the cropped or letterbox format. In the cropped format, there's nothing you can do; the bits they've sliced off the edges are gone. In the letter box format, you can view it as it is, or zoom the image to fill the screen (if your player has that option). However, zooming an image does magnify any deficiencies in the image quality.
If you prefer wide screen pictures, then buy 16:9 or widescreen versions. The 16:9 versions will have better resolution than widescreen letterbox formatted discs for standard 4:3 TV sets. If you prefer cropped pictures, then buy 16:9 versions (and expand the frame), or look for non-widescreen versions. If you see a disk marked as “VAR,” that means the aspect ratio is variable (the disc probably has a wide screen feature film, and non-wide screen extras, like documentaries).