Have you ever seen a photograph where everybody's eyes look really red? Well, that's called red eye and it's obnoxious.
There's a couple of ways to avoid getting red eye. If you're shooting with a DSLR chances are it's not going to be too much of a problem.
Red eye happens when the flash on the camera illuminates and blows out the eyes and you get that effect. Shooting with a digital camera most times you're going to bounce the flash off the ceiling and back down and that will eliminate the red eye.
But, if you are using a point and shoot like this or a digital camera with a pop up flash and you're firing straight into the face it could be a potential problem.
Now, a couple of ways you can avoid it are to have the subject of your photographs not looking directly into the camera. Have them look slightly off centered. And this is a really good way to avoid it.
In addition, a lot of cameras like this [guy] here have options for red eye reduction or to avoid red eye. And what they basically do is they're fire multiple flashes so that it tricks your eye into not getting red.
Now, if worse comes to worst and you've taken your family Christmas card or whatever and everybody has red eyes you can always really easily pull it into Photoshop or any editing program and clean it up.
Even really, really simple programs that come with your cameras like Cannon and Nikon and Sony they all have propitiatory editing software. Every single one of those has a really simple basic way to remove red eye which generally just means you have to click on the physical eye and it will suck it out and you'll look great.
Obviously avoiding red eye in the first place is the best way to go.