This was written originally in about 2005. It's a bit out of date in places.

1)Summary Digibox settings:
a) 16:9 --> This means leave picture as is. It might be 16:9 or 4:3
b) 4:3 Letterbox. --> Leave 4:3 alone, but put 16:9 into the middle of the frame
c) 4:3 Crop --> Leave 4:3 alone but chop of sides of Widescreen. Evil mode (IMHO)

First understand your TV.

There are basically THREE kinds of TV.
:: Original type TV with 4:3 screen
:: Widescreen TV (16:9 screen)
:: TV that looks ordinary 4:3 but can do 16:9 widescreen

What does 4:3 mean?
If the TV picture is 16" wide, it is 12" tall. The diagonal is thus by geometry = 20" (i.e. 5:4:3 triangle). This might in the past have been called a 21" TV. Now they are getting more accurate and it would be a 20" TV or 51cm

Thus a 40" 4:3 TV has a 24" high by 32" wide picture.

This is a similar shape to old pre 1950's cinema "Academy format" 35mm film. In the 1950s the Cinema introduced "Widescreen" due to perceived threat of television.

Cinema does Widescreen by three methods:
1) Matte on a normal shape film frame
2) Anamorphic lenes (Panavision method).
3) Special 35mm film (Super 35)

All methods can be combined.

What is "Matte"?
Say you take a photo and the scene has too much. You could crop of the sides, top, bottom (even changing the shape) to get a more "zoomed in" and better composition. It then could be reprinted at the correct size.

To allow latitude in filming, all films are shot taking in more of the scene than is ever shown. It is "matted" down to correct shape and amount of scene in transfer to prints for cinema.

What is "Anamorphic"?
It is using linear squeeze of the image (by example if you look through a tall parallel sides glass of water), to fit more width of scene in a normal film frame, the projector has a special lens to reverse the distortion and stretch the image sideways. On the film frame everything looks tall and thin. The "prints" may be also matted.

What shape is Widescreen?
Perceptive readers and cinema goers will realise Cinema WS can be almost anything...
Typically a ratio of 1.85:1 for moderate WS, to 2.35:1 for Wide Widescreen, to an increadible slit like 2.6:1 for Ben Hur!
TV Widescreen is a FIXED 16:9 = 1.78:1 ratio. Always less wide than Cinema!

TV Widescreen Transmission can be:
Any shape you like letterboxed in a 4:3 frame
OR
Any shape you like in an Animorphic 16:9 frame.

So:

* 4:3 image in a 4:3 frame fills the picture, and a regular TV, but has EMPTY black bands on the sides for a WS TV.

* A Widescreen picture "letterboxed" in 4:3 has black bands (or dark grey bands) top and bottom full of black lines on a regular TV. On a WS TV it has black bands all the way around, you can zoom in but the picture blurs.

* A 1.78:1 Widescreen picture in an Animorphic 16:9 frame has no bands on a WS TV, but looks too tall and skinny on a 4:3 TV.

* A 2.35 Cinema WS picture on Anamorphic WS has blank lines making dark bars top and bottom EVEN ON A WS TV!

SO WHAT DO I SET MY DVD player or Digibox to?

On Analog TV or VHS, the image is never Anamorphic (You can record your own anamorphic VHS though). This is so as to not upset normal 4:3 TV viewers. If it is "Widescreen", then the picture has "wasted" black lines. On a WS TV you need to "zoom" to fill the screen (Though if the Letterboxed image ratio is more than 1.78:1 then you still must have bands top and bottom, even on a WS TV).

On Digital (Sky, Digital MMDS, DVD, and Digital Cable) the image can be transmitted normal OR anamorphic, no matter what shape of image is in it!

The 16:9 setting:
The Digibox and DVD player 16:9 settings, essentially don't do anything!!!!! This means the 4:3 or 16:9 animorphic signal is passed through unchanged to the TV:
1) A regular 4:3 TV will be OK with 4:3, but with Anamorphic DVD (called "enhanced for 16:9 TVs on DVDs) or Sky Digital (e.g. BBC TV or Sky movies WS) the picture is too tall. Every thing is squashed in from the sides.

2) An advanced 4:3 TV with a 16:9 menu (many Sony, Philips, Mitsubishi, JVC and Panasonic, may manually or automatically shrink the height. You do get black bands, but they have no lines in them. All the lines are in the picture. The picture is identical to a WS TV.

3) A 16:9 WS TV will display the 4:3 material with blank bands at the side and anamorphic material the correct shape (fill the width).

(With a suitable SCART cable the Normal 4:3 /Anamorphic 16:9 WS switch ought to work automatically. With some DVD players and with Digibox via RF the Normal/WS must be done manually with a TV menu). If SCART enabled is OFF on the Digibox and the TV is not correctly connected via SCART, the 16:9/4:3 switch must be done on the TVv remote by the viewer.

The 4:3 Letterbox Setting:
If the DVD film or Digibox reception is a 4:3 signal (which might be a 4:3 "full screen" picture, or a "letterboxed" Widescreen image inside a 4:3 picture like VHS or terrestrial Analogue TV), then this setting does nothing.
If the signal is ANIMORPHIC, then the number of lines in the image are reduced by 3/4 by resampling the image and then superimposing it into a non-anamorphic full frame. If the original image was WS, then the result is like terrestrial "letterboxed" WS. This setting should ONLY be used with older or limited 4:3 TVs. Never with WS 16:9 TV, nor with modern 4:3 TVs that have a 16:9 menu mode, unless you are simultanously watching on old 4:3 TVs too in another room. On animorphic WS signals you lose none of the area of the picture but about 1/4 of the detail.

The 4:3 "Chop" setting.
This is horrid for films as you lose the sides. It is for viewers how feel their screen should always be "filled".
If the DVD film or Digibox reception is a 4:3 signal (which might be a 4:3 "full screen" picture, or a "letterboxed" Widescreen image inside a 4:3 picture like VHS or terrestrial Analog TV), then this setting does nothing.
If the signal is ANAMORPHIC, then you lose nearly 30% of the area of the picture as the sides are chopped off. No detail is lost.

Other Issues:
Sometimes the BBC transmits a 4:3 image inside a 16:9 anamorphic frame... This is daft as:
1) The WS TV user loses 30% detail and knows how to display ordinary TV pictures.
2) The old 4:3 TV user sees the picture with a black border all the way round, unless they are using the evil chop mode (And they lose 50% (letterbox) to 30%(Chop) detail.
3)The 4:3 TV with Anamorphic 16:9 mode gets the same quality of picture as (1) but it has a black border all the way around like the old TV user in Letterbox mode (but is much sharper).

Not all Widescreen images on Sky Digital are Anamorphic. Most Irish TV WS on Sky is transmitted 16:9 WS now, but 4:3 Cropped or 14:9 Letterboxed,  on terrestrial, losing 30% or more of the quality for WS TV and modern 4:3 TVs with the 16:9 mode on Analogue.

Saorview DTT will give Widescreen, with typical DTT setbox offering similar features to a Sky Digibox for 4:3 or 16:9 WS TVs.

Some comparisions: (very rough prices)
Nasty 28" 4:3 TV no 16:9 mode = 300Euro
Good 28" 4:3 TV with true 16:9 mode = 400 Euro
Decent 28" WS TV typically = 700 Euro
An average WS 32" TV = 1400 Euro
An Average WS 36" TV = 2500 Euro

Widescreen TV to give same size picture as 20" ordinary TV = 32"(€1,500)
4:3 TV with 16:9 mode giving almost a 27" WS image = 28"(€400)
Widescreen TV to give a regular 4:3 x28" image = 36"(€2500)

Conclusion 
Since almost all older TV and pre 1950 films  are approximately 4:3 and all commercial VHS is non-anamorphic you need to pick the Widescreen TV size based on 4:3 images.

If you can afford it the minimum WS TV if you are used to 21" TV is 32" NOT a 28". A 28" WS gives a VERY small regular image.

I'd recommend a minmum of a 36" WS TV. If you can't afford a 32" or 36" WS TV, then I recommend a BIG 4:3 TV that has a true 16:9 mode (The sales guy might not know. Play with the remote on the 28" and bigger 4:3 Philips, Sony, JVC, Mitsubishi and Panasonic). The WS animorphic picture on DVD or Sky Digibox on such a TV will be better than a cheap 28" WS and roughly the same size.

No matter what TV you get there will be black bands some of the time if the picture is the correct shape.

Make sure the Digibox or DVD player is in 16:9 mode NOT "4:3 letterbox " for a WS TV or 4:3 TV with WS/16:9 modes.

If your TV does 4:3 only, then "letterbox" on your Digibox or DVD shows all of the picture. You may miss important action, detail or dramatically impair the orginal artistic impact by selecting 4:3 crop.

WS Cinema often will have "bars" too even on a WS TV. Backlight the wall / ceiling behind the TV and dim or turn off the centre light. Chose a dark cabinet TV, then you see the "Original Aspect Ratio" picture just like in the cinema without consciousness of "bars".

If you don't have a WS TV or a 4:3 TV with 16:9 mode, by all means put the digibox in its 4:3 Crop mode to fill the screen, if you want a larger picture and don't mind losing the sides of the picture..

If you re-read the bit about "matte" and consider the phrase "open matte" you will understand why some cinema releases on DVD and VHS create the impression that the DVD has the top and bottom chopped! (The DVD ought to be closer to what was seen in the Cinema, with more area at the side missing from the VHS. The VHS *might* have some picture top/bottom not seen in Cinema or DVD version... the director didn't mean it to be seen, it is to avoid chopping the sides too harshly).