This topic pertains to almost every camera, including your point-and-shoot ones. Have you ever gotten really grainy looking images and not been entirely sure how that happens? The culprit is ISO. Every camera has a threshold of how high the ISO number can go before it starts to pick up too much grain.
ISO used to be the film speed on a roll of film. Today, this is something you can change with each individual photo you take on a digital camera. Most consumer DSLR cameras will let you go up to 600 or 800 before the image starts to look poor (the dial may turn higher, but you won't love those photos unless it's just an urgent situation). If you're in perfectly fine daylight conditions, I'd keep this down at 200.
So why do we turn the ISO number up at all? Well, remember that our three variables are shutter speed, aperture and ISO. If you're in a dark situation, and you want to let more light in to the camera, you want to do one, two or all three of these things:
Slow down your shutter speed (so it stays open longer)
Open up your aperture (the low numbers provide a bigger opening of light)
Increase your ISO (greater sensitivity to light)
If you're shooting in an indoor ice rink (thanks for the question!), chances are that you still want your shutter speed fast enough for sports action (maybe 200, aka 1/200th of a second). You can dial down your aperture, since you just want your child most in focus, but is that enough to get that line to the middle of your exposure scale?
Now you've got a third trick up your sleeve - increase your ISO! Dial this number up, and you will have the ability to keep your shutter speed where it is. Get that line in the middle, and shoot!
Why not try this tonight while hanging with the family over dinner? Better to get to know your camera when it's not an important situation... how high does your camera want to go with its ISO?
Nikon users: I hear your camera may default to an "auto ISO" setting, so make sure that's off.
You may not see grain in your photos until you download them to your computer, and even then maybe only when the photo is blown up to a larger size. What you plan to do with the photo is definitely one factor to consider.
For the more advanced shooter and editor, here's a little thing I figured out over time... if I'm going to increase my ISO pretty high, it's important to nail the exposure then and there. You can't get it "most of the way" and then lighten it a ton in Photoshop later, because the grain will become all the more ghastly. I have a hard time trusting that my professional cameras can reach above 2000 or even 3000 ISO, but I'm learning that it still can look great if I get it right in-camera. So go all the way if you can!