a photography technique for combining flash light and natural light.
A flash photograph will use the synchro speed setting of the shutter. This results in the shutter being open for the minimum possible amount of time, and in the scene being lit primarily by the flash itself. For example, suppose that you are shooting in your typical dusk situation; the light meter suggests an exposure of, say, f4 1/4. Your camera has a synchro speed of 1/125. You shoot at, let's say, f4 1/125. This means that ambient light will be underexposed by about five stops, which means that it will be hardly perceivable. What you get in the end will be controlled almost completely by flash light.
This often results in an appearance that people do not like. In particular, it tends to emphasize what is right in front of the camera and completely kill any distant background.
In slow sync you set the shutter to a slower speed; in the example above, you could set your camera to f4 1/8. This will allow appreciable exposure of the parts of the picture lit by natural light.
If you employ really long exposure times, such as 1 second, and shoot handheld you will get interesting pictures where the flash lit parts are very sharp, and everything else is exposed but blurry because of hand motion. Additionally, you will get interesting color casts, because the available light will frequently have a different color balance than the flash light.
In many automated cameras, the slow sync setting has an icon of a person in front of a mountain background - the idea is that you will be able to have both the archetypical subject (your SO) and the archetypical background (the majestic mountain) in the picture.
In fancy cameras, you can decide if you want the flash to go off at the beginning of exposure (front curtain synch), or at the end (rear curtain synch). This makes a huge difference for pictures with moving objects - if you want to have proper looking trails you need rear curtain synch.
Slow sync is a nice, if occasionally overused, technique. It is a bit unpredictable, though. Experiment and bracket.
See also: flash, shutter, exposure, T, X, B.