Fill flash
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Fill flash is using a portable flashgun to supplement the available light. When pros have the flashgun mounted on the camera, they are most often using it for fill-flash.
The basic idea is that you set your shot up for the best overall light balance using available light, and then brighten the main subject -- which may be in shadow because of the way you've got the rest of the shot set up -- by setting the flash on the camera to a lower value than normal, typically -1 EV (one stop less).
Advanced flash guns such as the SB 800 and SB 900 can set the value automatically using the Balanced Fill Flash function.
You most commonly use fill flash when photographing people. So, for example, you could have someone standing with their back to the sunset, which will show up blonde hair very nicely. Without fill flash, this scene would come out either hopelessly overexposed, if you exposed for the face, or with the face underexposed. With fill flash, the face will be correctly illuminated. As a bonus, you get the all important catch lights in the eyes.
Fill flash works best if you use some kind of light modifiers to reduce the harshness. You can use a Gary Fong Lightdome, or the reflector card on your flash gun.
With fill flash it is important to balance the colour temperature. Stick a gel over the flash to match the colour of the ambient light. If you are shooting in a room illuminated by tungsten light then a tungsten converting gel should be used, which is an orange-yellow. If you are shooting a room illuminated with fluorescent light, use a greenish gel. Gels of these kinds are supplied with the SB 800 and SB 900. If you write to Lee Filters, they will send you a sample pack of all their Gels, which are large enough to put on Nikon flash guns. If you don't balance the colour temperature, some parts of the picture will have a colour cast which cannot be edited out in postprocessing.
