Shutter speed is the time is takes for the shutter to open and close.
With film based cameras it was the amount of the time the film is exposed to light. For digital cameras its the amount of time the sensor can see the sceen.
Shutter speed is measured in seconds, usually fractions of seconds. A larger denominator gives a faster shutter speed i.e. 1/100 is slower than 1/1000.
Shutter speeds slower than 1/60 will result in image blur unless the camera is held steady using a tripod or something similar.
Apature and shutter speed go hand-in-hand as they both control the amount of light reaching the sensor. You need to take this into account when getting the right exposure.
Very slow shutter speeds such a 1 or 2 seconds are usually used in very low light conditions.
Shutter speed can be used to give the impression of motion. A fast speed will freeze the image, however a slow speed introduces blur which gives the illusion of motion.