The shutter speed determines how long camera sensor is exposed to light. For instance, a shutter speed of 1/125 will expose the sensor for 1/125th of a second. Shutter speed affects motion blur and exposure.
The faster the shutter speed the less blurry the moving subject in the image will be. Usually, a shutter speed of 1/1000 will freeze most moving subjects. A rule of thumb is to keep your shutter speed equal or faster than 1/60 for hand held shots. Slower than that usually integrates camera shake thus creating a blurry image.
The faster the shutter speed, the less time light has to hit the camera sensor thus affecting exposure.
Here’s an example of a fast shutter speed (1/1000 sec) freezing the moving subject:
Here’s an example of slow shutter speed (5 secs) with a blurry moving subject: