When you press the shutter button on your camera and take a picture, the aperture blades take a specific amount of time to close. This amount of time is known as your shutter speed. Generally it is a fraction of a second, and if you’re capturing fast motion it needs to be at most 1/300th of a second. If you’re not capturing any motion, you can sometimes get away with as long of an exposure as 1/30th of a second. When you increase your shutter speed—the length of time where the sensor is exposed to light—two important things happen.
First, the sensor is exposed to more light because it’s been given more time. This is useful in low light situations. Second, the sensor is subject to more motion which causes motion blur. This can happen either because your subject is in motion or because you cannot hold the camera still. This is fine if you’re photographing a landscape at night and the camera is placed on a tripod, as neither the camera nor your subject is going to move. On the other hand, slow shutter speeds pose a problem when you’re shooting handheld and/or your subject is moving. This is why you wouldn’t want a shutter speed any slower than 1/30th of a second when photographing handheld (unless you’re known for your remarkably still hands).
In general, you want to use the fastest shutter speed you can but there are plenty of circumstances where you’d choose a slower shutter speed. Here are a few examples:
These aren’t the only reasons but a few common ones. The important thing to remember is a slow shutter speed means more light at the risk of motion blur. A fast shutter speed means low risk of motion blur while sacrificing light.