Last week I talked about aperture, the shutter opening in your lens that controls how much of your image is in focus, as well as the amount of light that reaches the sensor. Your other control over the amount of light reaching the sensor is shutter speed. Shutter speed is simply the length of time that the shutter is open and thus letting light onto the sensor.
A fast shutter speed allows you to freeze motion, so that a moving object can appear stationary in the image. A slower shutter speed allows you to show motion with blur effects. A very slow shutter speed will show even more motion but may also introduce unwanted camera shake (the slight unintentional movement of your hands while taking a photograph).
As a rough guide, here as some typical shutter speeds and examples of when you might use them:
1/2000 second - To freeze the motion of birds in flight
1/1000s - To freeze the motion of motor vehicles
1/500s - To freeze the motion of sports such as running
1/125s - Panning shots of vehicles
1/50s - Minimum for typical use (50mm and shorter lenses)
1/15s - Panning shots of runners
1 second and longer - Soft water effects and night images, on a tripod
In general use when you're not using a tripod and simply want a sharp image, the minimum shutter speed you need in order to avoid camera shake depends on the lens you're using (or how much you have zoomed in using a zoom lens). As a very rough guide, 1/35s is fast enough for a 35mm lens, 1/50s for a 50mm, 1/100s for 100mm etc.
If you've been trying out 'aperture priority' mode, whenever you changed the aperture setting your camera has immediately adjusted the shutter speed so that the image remains at what the camera things is a correct exposure (how light or dark the image is).
You can take control of your camera's shutter speed by either switching to 'shutter priority' mode (in which case the camera will control the aperture for you) or manual mode (you control both aperture and shutter speed). Remember that this is a creative decision. Do you want to manually control the depth of field (aperture), or manually control the amount of blur/motion effect (shutter speed)? If you switch to manual mode, it's now up to you rather than the camera to get the image as light or dark as you want.
So that, simply, is shutter speed. If you don't have a tripod and the scene is too dark even at your widest aperture and slowest reasonable shutter speed, then you have one more option which is to change your ISO setting. And I'll talk more about ISO next week.