The best way to understand is to try it out.
Grab your camera and set it to Aperture Priority mode (Av).
Set your aperture value to f5.6.
Then, adjust your ISO to 100 (On the 50D, this is done by pressing the button next to your top screen and then turning the top dial).
Take a photo.
Then, turn you ISO up to 400. Aim your camera at the same thing you did in the last photo.
You should notice than your shutter speed got faster. About 4x faster. ISO100 -> ISO200 -> ISO400 is two stops, therefore your shutter doubled twice.
Then, turn up the ISO to 1600. Once again, the shutter should double twice.
Then, just for fun, try out ISO 3200. Should be double the speed of 1600.
Now, here is where you will meet your enemy, digital noise.
Load the photos on the computer, and then look at the ISO 100 shot at full size (100% crop). Then look at the 400, 1600, and 3200 the same way.
What do you notice? Ugly right?
Generally, you want you ISO to be as low as possible WHILE maintaining a usable shutter speed. "Usable Shutter Speed" means a speed that will capture your subject without blur. This includes you. Your hands shake a little, even when you are trying to hold still. Slower shutter speeds suffer from this, and therefore will blur.
But in the world of sports, you're not just worried about you shaking hand. You have subjects that aren't stopping to say cheese. They are moving fast. Therefore, in this instance, a "usable shutter speed" is much faster than a normal photo. Most sports that I shoot, I try to keep it up around 1/1250th or faster.
Now, there are some cases in which you WANT your photo to blur. This could be water flowing down a creek, or a fountain, or a racecar.
What!?! A Racecar?
This involves a more complicated technique, called panning. Here, you intentionally slow down your shutter to show movement in the photo. But, in order to pull it off, you have to move your camera with your subject at the same speed. That way, the subject stays sharp, but the moving parts blur out.
"The good, the bad, and the Money Shot"
Here are some examples from my most recent shoot at Infineon Raceway in Sonoma, CA.
Good- Sharp Photo, but is the car moving? Great shot if you want pictures of parked cars.
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Bad- Slow Shutter, didn't pan the shot:
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The Money Shot- Slow Shutter with a good pan, lots of "motion"
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