I have heard of a technique called "killing the ambient" in flash photography. What does it mean and how do I do it? This similar existing post I believe is separate enough to warrant this question - What exactly is flash sync speed, and should it be a factor in a buying decision?
How to kill the ambient light
"Killing the ambient light" is a term used when you want to take a picture that is purely lit by flash, so that you have complete control over the lighting in the picture you are taking. It follows, therefore, that if you were to take the image without the flashes enabled, the image would be very heavily/completely underexposed.
Normally, this would be achieved by first selecting the aperture that gave the desired depth of field to the image, before increasing the shutter speed (decreasing the exposure time) until all ambient light is removed. This is the exposure that we will use when we take the final shot.
Now we can work on lighting our subject using flashes. Using the flashes in manual mode, I would gradually increase the power until the subject was lit as I wanted.
In Syl Arena's "Speedliting Pizza" article, he shows how he used this technique to remove the fluorescent strip lighting in a kitchen, so that he could use directional light to improve the appearance of his subject (pizza in this case). What I find particularly useful is the image that is taken at the exposure and with the same flash settings as the final shot, but zoomed out; this really shows how the pizza is properly illuminated by the flash, whilst everything else in the room is underexposed.
When there is a lot of light, outdoors for example, you may well want to have a very faster shutter speed to kill the ambient. One complication that can arise is that the sync-speed (The fastest shutter speed that can be used with a flash in manual mode) of most DSLRs is between 1/125 and 1/250 of a second. The reason for this limit is because of how the shutter actually moves, and how flashes deliver light.
When taking a photo at a normal/slow shutter speed, the first curtain moves, leaving the shutter "fully open". Towards the end of the exposure, the second begins to move, closing the shutter. When using conventional flash sync, the flash would be fired whilst the shutter is fully open (either immediately after the first curtain, or so that the burst finishes just as the second curtain begins to move).
When taking a photo at high shutter speeds, at no time is the shutter fully open; the second curtain chases the first curtain, meaning that there is only a slice of the image being exposed at any instance, and firing a flash would mean that only the slice of the image where the shutter was open at the time when the flash was fired would be correctly exposed. This is where you need to use high-speed sync.
High-speed sync can only be used with certain flashes that support your cameras flash protocol (E-TTL for Canon, i-TTL for Nikon, etc.). What it allows is for the camera to fire continuous, lower powered flash over the full duration of the exposure, rather than one lump of light as is the case with manual flash, as shown in this diagram by Canon
So when you want to kill the ambient light and use a very fast shutter speed, you'll adopt the same basic process as before, but instead of using the flashes in manual mode you'll want to use E-TTL and high-speed sync. Syl Arena covers this technique in his two-part article "Killing the sun" which can be found here and here.
You 'kill the ambient' when you set the flash(es) power high enough so that at the chosen aperture, shutter speed and ISO the contribution made by ambient light is insignificant to the picture. In other words, taking the picture in full darkness with flash only while all other variables are the same would give you the same result.
What does it mean? As Miguel says, it's overpowering the ambient light entirely. Indoors you can usually do this by increasing the shutter speed to the maximum sync speed of the camera (usually 1/200th or 1/250th). Increasing the shutter speed won't affect the flash exposure because it is so much shorter duration than the shutter speed. If that isn't enough, you drop ISO, use a smaller aperture or increase the flash power.
You might do this indoors (or out) if you have mixed light sources, incandescent, sodium, flourescent, sunlight. Getting white balance right can be impossible, so by killing the ambient you just have to worry about one light source.
Outdoors, with a speedlight, killing the ambient can be difficult. The ambient exposure at the lowest ISO is likely to be 1/200th at f/8 to f/16, so there isn't much room to work with. You either need a very powerful speedlight, or multiple speedlights, very close to the subject.
Just to clarify the jargon, "ambient" light is the existing lighting.
Most flash photography captures some form of balance between the flash and the existing (ambient) light, as MikeW said a common reason for wanting to overpower the ambient if it is the wrong colour.
You can control ambient light by controlling the shutter speed. Which means, if you increase your shutter speed very high, there will be barely some light entering your camera. Now to properly expose your subject, you can cast light using flash. And you can even control the amount of light from your flash entering your camera by using aperture (f stop). Increase the aperture to let more light in, decrease the aperture to let less light in.
Using these tricks, it is possible to simulate a night shot(or a flavor of that) in day light :)
I think Edd has given you a very good, if not perfect explanation of how the flash works.
But with respect to "killing the ambient":
In normal photography, you make use of the ambient light, which due to the nature how sensors capture light (linear vs. logarithmic in the human eye) can mean that a scene will be black in the darker parts and white in the brighter parts, though you have seen it as a scene of darkness and brightness.
When utilizing a flash, you will often improve the lighting of a scene, primarily adding light to the dark scenes, hence if you do it skillfully, only a fellow photographer will be able to tell that a flash has been used.
The ambient light dominates the scene, allowing you to capture the ambiance of the location you have photographed.
If however, your flash overpowers the ambient lighting, you will loose the ambiance as well as the ambient light. In many cases your scenes will look rather bad, especially in direct flash (compact camera look of flash in a dark room), but I am sure you can use it creatively to create an effect you want, especially if you use coloured gels.
if you use ptl or what ever you camera mfg calls it,as if you are going to fill flash and you need to be in av mode,and you first check what the camera's says for a non flash image lets say 125 at f8 then you turn on the flash but set the aperture to f16 your flash will light up the subject but you will under expose the ambient = kills the ambient. A one stop shift makes a brides dress pop with out looking like flash being used