Shutter speed is the setting that determines how long the camera shutter is open, thus how long the sensor (or film) is exposed to light. The smaller the number, the greater the “freeze-frame” effect. A really small fraction of a second can make almost any subject free of motion blur, though that effect also depends on other factors such as distance from the subject, whether you have a telephoto lens or a wide angle lens, and for modern cameras the image stabilization that is involved.
When trying to get motion blur intentionally, then a longer shutter speed is desirable. This is how you would get that milky look that is used with streams, waterfalls and even cyclists. Longer shutter speeds are also used to get the red light blur of automobiles on a road/highway.
Long exposures are also frequently used in landscape photography to allow greater depth of field. The “rule of thumb” to use when hand holding a camera is that the shutter speed should be equal to or faster than one divided by the focal length of your lens. So if you are using a 200 mm lens, your handheld shutter speed should be faster than 1/200th of a second. This is effected by your personal shooting style and stability, and also the image stabilization of your camera and/or lens. It also becomes a bit less universal as you get into longer telephoto lens lengths. To get high quality images that you can enlarge to sizes such as wall posters, you should use a tripod whenever you are even close to the limits of that old maxim, however if you are certain that your images are only EVER going to be used in low-resolution situations (such as website graphics) then you can push the limits just a little bit.
This rule can quickly and easily become customized to your needs as you gain a little experience with your own image quality. You should be able to determine if your steadiness is adequate or exceeds your needs for sharpness, and adjust accordingly. And of course, have fun with your photography.