Shutter speed is the amount of time that the shutter is open.
In film photography it was the length of time that the film was exposed to the scene you’re photographing and similarly in digital photography shutter speed is the length of time that your image sensor ’sees’ the scene you’re attempting to capture.
Thanks to Mr.Google for this image.
Shutter speed is measure in seconds. The bigger the number, the faster the shutter close. For example, 1/4000 is faster than 1/50. It's usage is depends on whether and lights. If you are using speed lower than 1/60, you will need to use tripod if your hands shaking or some types of image stabilization like IS(Canon), SteadyShot(Sony), or VR(Nikon).
Shutter speed is depends on your type of composition where you want to take a long shot (eg. slow shutter speed light trails) or fast shot (eg. freeze motion, fast speed). Some cameras will give you slow shutter in low light due to small aperture lens (eg. f/4.5, f/5.3, f/6.7) and will force you to use flash or tripod to make the image stable.
Focal Length and Shutter Speed is another thing to consider when choosing shutter speed is the focal length of the lens you’re using. Longer focal lengths will accentuate the amount of camera shake you have and so you’ll need to choose a faster shutter speed (unless you have image stabilization in your lens or camera). The ‘rule’ of thumb to use with focal length in non image stabilized situations) is to choose a shutter speed with a denominator that is larger than the focal length of the lens. For example if you have a lens that is 50mm 1/60th is probably ok but if you have a 200mm lens you’ll probably want to shoot at around 1/250.