Shutter speed is just that - the speed at which the shutter closes to stop light getting to the sensor/film. It is how long the sensor is exposed for.
A slow shutter speed lets more light in so the photo will be brighter, but it also means that any movement is recorded as a blur. A fast shutter speed captures movement sharply but sacrifices the amount of light hitting the sensor.
Shutter speed is measured in seconds or parts of a second, for example 1/100 means one one-hundredth of a second. 1/30 means one thirtieth of a second. The bigger the number after the "1/", the faster the shutter speed. It also can be slow enough to count in whole seconds, such as 1s, 2s, 4s, 15s, 30s.
How is shutter speed used then?
Aside from letting in the correct amount of light, shutter speed can be used for creative purposes.
A slow shutter speed will show motion blur. This can create interesting images of motor racing, or running water etc. A really slow shutter speed (for example 10 seconds) can be used to capture light trails from cars.
A fast shutter speed can be used to freeze motion which is particularly useful when shooting vehicles, sports, and even portraits and weddings. Have you seen those nice pictures with confetti around the bride and groom? Fast shutter speed! A flash gun works well with a fast shutter speed as the image will tend to be darker so may need extra lighting.
As with ISO and Aperture, when the Shutter Speed is changed it changes the exposure of the image, so the ISO and/or Aperture will need adjusting to compensate.