Camera conundrum

My question: Why does higher ISO on a camera mean less blur?

I wonder if the 3-4 readers of this blog know the answer. Not that I need to know the ins and outs of this stuff, but well, I am curious...

My digital camera manual says that a higher ISO will mean less blur. I usually keep mine on 400 or 800 in case I want to snap a shot of something fast-moving. Technically, a higher ISO increases the camera's sensitivity to light and images, so in a low-light area or in a situation where you want the shutter speed to be faster, you'd want to increase the ISO to let more light register. Fine with me, but I don’t understand why that would mean less blur. If a higher ISO lets in more light and is more sensitive to images ("noise"), wouldn’t it show MORE blur??

The camera also allows me to decrease the shutter speed to let in more light, but not to increase it. If I want to let in more light, I can decrease the shutter speed, but I better not shake the camera. If I decrease the speed, the camera automatically lowers the ISO to decrease the sensitivity to noise and graininess. But then, there will be lots of blur. Why won't my camera let me increase the speed, though?

It seems to me in action shots, you’d want a faster shutter speed. But again, they recommend increasing the ISO instead, to cut down on blur. And again I ask, why would more sensitivity to light and other images mean LESS blur and not more? Wouldn't it make more sense to have a faster shutter speed to cut down on blur, than a higher ISO?

Maybe I'll ask my photo-taking friend Sarah about this, or someone at work.

UPDATE

note to self. wikipedia says:

"halving the shutter speed doubles the exposure (1 EV more), while doubling the aperture (halving the number) increases the exposure by a factor of 4 (2 EV). For this reason, standard apertures differ by √2, or about 1.4. Thus an exposure with a shutter speed of 1/250 s and f/8 is the same as with 1/500 s and f/5.6, or 1/125 s and f/11.

In addition to its effect on exposure, the shutter speed changes the way movement appears in the picture. Very short shutter speeds can be used to freeze fast-moving subjects, for example at sporting events. Very long shutter speeds are used to intentionally blur a moving subject for artistic effect.^[2] Short exposure times are sometimes called "fast", and long exposure times "slow".

Adjustment to the aperture controls the depth of field, the distance range over which objects are acceptably sharp; such adjustments need to be compensated by changes in the shutter speed."

Update 2:

I got an answer to my questions on the net... here.

I am still a bit confused, though. Let's say I set my camera at a high shutter speed to capture a fast-moving image. I then set the ISO high to prevent blur and let in as much light as possible at that speed. Will setting it high cancel out the shutter speed to begin with? And will it not always make a diff anyway because there's only so much light that can be let in if the shutter speed is fast?