Setting blacks (and whites) properly can be a little complicated. But the first rule of thumb is that whatever looks better TO YOU is likely the proper setting (once your eye is used to just how good a calibrated image can look). You can use Avia or DVE to test how far your preferred setting is from a given "reference" setting and to return to your preferred setting in a precise manner.
"Black" is encoded on the DVD as digital 16. The "Blacker than Black" bar is encoded on DVE as digital 7. The other two bars on DVE are digital 21 (the inner bar) and 25 (the middle bar).
On Avia the dimmer moving bar is digital 19 and the brighter bar is digital 21.
Blacker than Black detail represents light levels that were recorded below what the cinematographer and DVD editor chose to arbitrarily identify as "Black" for reference and quality control purposes.
Technically, Black and Above detail should always be visible and Blacker than Black detail should *NOT* be visible -- although it needs to be present so that the signal processing that happens before the pixels light up can take advantage of it. So technically you should adjust things so that digital 17 and above (only) are visible against a black, digital 16, background. If you raise Brightness beyond that point, Blacker than Black details (below 16) become visible as kind of darker "holes" in a now slightly grayish "Black" background.
If you adjust with DVE so that the Blacker than Black bar JUST becomes invisible, then you probably are still showing some levels of Blacker than Black data between 8 and 16 since you have made 7 your point of invisibility. If you adjust with Avia so that the dimmer moving bar is JUST invisible (i.e., as the Avia narration suggests) then you are possibly concealing data in the range of 17 to 19 since you have made 19 your point of invisibility. Meanwhile Guy Kuo of Ovation recommends raising Brightness a bit further for digital displays so that the dimmer moving black bar in Avia is JUST BARELY visible -- and so do I. Which is better?
THAT is a question of what the guys who produced the DVD INTENDED you to see!
You see the guys who are setting the balances when the DVD transfer is made are not so much trying to hit some mathematically perfect setting as they are trying to predict what the result will look like on your TV. That's because they are trying to hit a compromise that will work across the entire dynamic range of the film.
Now it is most typically the case that quality control for DVD transfers is done by watching the results on CRT based monitors, partly because that's what they have to work with and partly because they assume that's what most of the buying audience will be using. CRT based monitors have "floating" blacks -- black levels that rise and fall according the average brightness of what's on screen at the moment. So they assume that when the resulting DVD is played at home certain "Blacker than Black" details will float into view in scenes with medium to high brightness and will be concealed in darker scenes, and so they keep tweaking the black level on the transfer to try to get the visible level of detail "just right" -- based on the "float" that's happening in THEIR monitors.
Which means that no matter what level you set on your TV at home, you won't see precisely what they intended you to see unless your TV happens to have exactly the same degree of "float" as their studio monitors!
Digital displays such as LCDs and Plasmas typically have no "float" -- although there are some very few digital displays out there which are designed to emulate the "float" of a CRT. Now "float" is not really a good thing. Ideally a display would have no "float". But since the DVDs are made assuming your display has this flaw, you may need a compromise setting in your "better engineered" display in order to see what the DVD producers intended you to see.
The Avia moving bar chart is made with a half screen of gray to trigger a certain amount of "float" in TVs that do that. By making the leftmost moving bar JUST invisible, you have achieved a compromise setting that works across a fair range of CRT based systems that have a common degree of float. That is, you have set a black level that's deliberately a little too low knowing that it will float up. Avia includes variations of the moving bar pattern that have different amounts of stuff on the other half of the screen so that you can check just how much "float" seems to be affecting your black settings. One such pattern is totally black except for the moving bars. Another has a bright white half screen and a third has gray steps on the right side. Check all 4 patterns to see how the two moving black bars increase or decrease in visibility at any given set of level settings. You will need to get up close to your screen so that the sensitivity of YOUR EYE is not altered too much by the brightness on the other half of the screen.
For a digital display without "float" that Avia setting -- as described in the narration -- is too low. You will lose some black details you were supposed to see. So instead target a bit higher Brightness where the leftmost moving bar is JUST BARELY visible above the black background. Again you can use the other charts to double check whether your TV has "float" or not.
So is the DVE narration just wrong? No.
You see there's another school of thought which says that for digital displays without "float" what you really want to do is to make a compromise setting that's deliberately set a bit TOO HIGH so as to force some Blacker than Black detail to become visible! If you make the Blacker than Black bar in DVE JUST invisible, then you have made the top half of the Blacker than Black range -- from digital 8 to 15 -- just barely visible. The idea is supposed to be that bringing some of this Blacker than Black detail up into visibility will better match what the DVD producers intended you to see IN BRIGHTER SCENES where that stuff WOULD have floated into view if your TV only had some "float". But on the other hand, setting it that way means you will see TOO MUCH Blacker than Black detail in darker scenes -- which could yield noisier dark scenes since the quality control on Blacker than Black data is lower all along the reproduction chain.
Others say these folks are simply "thinking too much" and should just relax and set the display to the "proper" level where 17 is visible over 16 and 15 is not visible under 16 -- and then go buy good DVDs where the editors weren't trying to second guess how your TV works so much.
So how do you choose which is really best for YOUR TV?
Well of course the big test is what looks best to you while watching movies. But there are some other tests. First, digital displays (and to some degree CRT systems) aren't equally good at divvying up the gray scale range for all pairs of black and white end points. If you have several candidate setting pairs of Brightness and Contrast, one way to choose between them is to look at the Black to White gray scale ramps (or the higher detail, partial range, "reverse" gray ramps on DVE) to see which candidate setting produces what looks like the smoothest gray ramp.
A professional would do the same thing when measuring gray steps with a light sensor to try to achieve the best linearity across the range of the gray ramp.
Also, some TV's will have inherent limitations on just how far you can raise Brightness. You know of course that if you raise white levels with Contrast too high you may run into limits of your display -- points you don't want to cross -- points which you need to remember as upper limits for how far you might choose to raise Contrast. For example, you might see blooming on a CRT system or your might see thresholding (loss of white detail) on a digital system. Well some displays have limits on how high you can set Brightness. On those displays if you try to raise the base black level too far the display gets into a kind of rounding error as it tries to raise the over-all light output of "Black" a tiny bit. Digital displays have only a fixed number of steps of light output for each pixel, and so if the display wants to raise the light output just a little bit it has to barely turn on only a scattering of pixels. So if you get up close to your display and see widely scattered pixels just barely turned on in a nearly regular pattern (usually green or purple) in what should be "Black" then you know you have Brightness set too high. And thus that will become an upper limit on how high you can raise Brightness for your setup. Keep in mind that Brightness and Contrast interact so you need to check this for each pair of settings.
Finally there's the problem that not all source content is created equal. This is particularly so when watching broadcast TV. For broadcast TV, and for some cases of poorly produced DVDs, you will need to decide whether you want to (1) calibrate for perfect content and let the imperfect stuff look not quite as good as it might, or (2) pick a compromise set of settings that is not as good as it could be for perfect content but is less likely to annoy you when watching less than perfect content, or (3) save a few different sets of settings so that you have a "perfect" set and also settings that seem to work better with crappy source content.
Personally, I recommend calibrating for high quality, "perfect", source content and letting the crappy stuff look as bad as it wants to.