Camera shutter speed question...?

Okay so I'm kinda confused about this right now.
If i slow down the shutter speed by 20 seconds, or any amount of time really, how does it change the exposure?
Because on my camera, a GE A730, if i go to [menu>slow shutter>manual] it goes to a screen that says "long exposure period" and i can choose 1-20+ seconds [i have it on 20 right now]. Does that mean that at that speed i can take pictures of things like dripping water, and it'll show the individual drips?
Any help will be appreciated.

No, a slow shutter speed will have the opposite effect. It will not freeze motion, it will introduce motion blur. The shutter speed is how long the shutter will be open (and therefore the length of time that the film or image sensor will be exposed.) To freeze fast moving objects like water drops you will need a fast shutter speed.

A slow shutter speed (like the 1-20 second options you are looking at) will cause moving objects to appear like streaks in your picture. It can be used to make waterfalls look smooth like this:
http://flickr.com/photos/darbcu/33538724...

or it can be used to make cars driving at night look like streaks of light like this:
http://flickr.com/photos/priority/364971...
or
http://flickr.com/photos/soaring_is_sexy...

or it can make people look like a blur of motion like this:
http://flickr.com/photos/pnina_e/1893093...

To achieve most slow shutter effects you will need a tripod or other steady surface to hold the camera exactly still so that the only thing with the blur in the picture is the moving object.

See this link for more information:
http://www.ephotozine.com/article/Camera...