Shutter Speed

Although we call it shutter speed, its actually the duration for which the shutter remains open to let in light.
Obviously, a shutter that remains open for 1/100th seconds lets in twice as much light as a shutter that remains open for 1/200 seconds.
Shutter speed allows us to control a vital aspect of photography-> Motion.
You can use a fast shutter speed to freeze a moment in time, or use a slow one to show motion blur.(movement)
The shutter speed you choose will depend on what you are trying to show, whether blur or stillness, and also on the speed of your object. Keep experimenting with it. Its one of those things one learns best with experience.

There is a rule which says the shutter speed should be faster than 1/(35mm eq. focal length of lens) for a handheld photo, to try and prevent blur due to hand movement. But some of us are steadier than others. Try and find how for how long u can keep the camera still on a given focal length so that >70% of snaps at that shutter speed are sharp.

(On my 50mm lens, which gives ~80mm(35mm equivalent) due to the 1.6X crop factor, I can manage quite well upto 1/30s. slower than that, I do get some blur)

a few more interesting things-> Slow Sync Flash: Using a slow shutter speed like 1/10 s to let in ambient light, but the flash also fires in the beginning or end, depending on whether you've set it to front curtain or rear curtain respectively.
Rear curtain is interesting as it allows motion to flow and freezes it at the last instant.
Heres an example of slow sync with rear curtain (A pic I took in spree '10) :

There is one more aspect of using flash and shutter speed. Many cams, especially DSLRs, theres a certain shutter speed, above which the flash wont fire. On my canon 400D its 1/200s. So be careful when using fill flash outdoors, the flash will not fire if u use a shutter speed of say 1/500s., unless you use an external flash and put it to 'high speed sync'.

The reason for this phenomenon is this(read if you are curious): The shutter has 2 curtains. For a shutter speed of say 1/10s, initially the first curtain opens exposing the top part of the sensor to light first. After it opens completely, the second curtain closes, blocking light from hitting the top of the sensor first and eventually covering it up completely. This lets every pixel on the sensor be exposed for the same duration of time... The same process happens upto about 1/200s. At one point int time, it became difficult for shutters to cross this 'speed barrier'. But then, camera manufacturers came up with this trick for speeds faster than 1/200s. As the first curtain reveals light, before it has completely opened, the second curtain starts closing. Its effectively like a moving slit that allows light to pass through to any given pixel only for that short duration of time. this slit moves from top to bottom.

Now consider using a flash in such circumstances. The duration of a strobe of the flash is very short (~1/10000s or less). If the flash were to fire, you'd get a brightly lit rectangle in the image with the rest of it only exposed to ambient light! To protect you from this, the camera will not allow you to choose a shutter speed >1/200~1/250(depending on your model) when the flash is on.

(High speed sync flashes actually reduce the power of the flash, but the flash lasts for a long duration of time-(via multiple short synced bursts) enough for the slit to scan over the whole sensor)