Sutter Speed or Exposure Time is the amount of time the shutter stays open in order to let light go onto the sensor.
What exactly is the shutter? you ask, well, it's like a little curtain in front of the camera sensor that opens and closes at the speed you want. It can open up as fast as a 8000th of a second (1/8000 s) in many cameras. At those super fast speeds you can pretty much freeze anything, for example: water falling down.:
Fast shutter speed means that you can freeze the movement of an object, but at the same time, it means that less light will be able to reach the sensor, if every other variable is kept the same, this means that the exposure (picture) will be darker.
Makes sense right? the less time the less light, so the darker the picture.
Long Exposure: Pictures with a slower shutter speed
After you slow down the sutter speed, you achieve what's known as a long exposure. These pictures will gather more light, and at the same time, moving objects will be blurred. Let me show you a cool example of this:
This picture was taken at 11:30pm at night, the mango source of light is the moon! The pictures was taken with a shutter speed of 20 seconds, that's why the water looks so calm, after time and light passes, the moving objects (water in this case) get blurred and so the loose detail, water usually looks like mist.
Find more examples of long exposure photography in the Neutral Density Filter tutorial