ISO stands for International Standards Organization, which isn't really a photography term. It is the standard scale for measuring light sensitivity on the sensor in the camera. Originally it was for how light sensitive the film in a camera was.
For us photographers, the easiest way to put it is thus: The lower the ISO, the less sensitive it is. The higher the ISO, the more sensitive. Having a standard for sensitivity is important as it means that you can shoot the same ISO on different cameras and know that the exposure will be the same.
So what does this mean in practical terms? With low ISO, the shutter speed will need to be lower and/or the aperture wider to let in more light. The quality of the picture will be its best.
As the ISO is raised, the sensor picks up more light so a faster shutter speed and/or smaller aperture can be used. However, the sensor will also pick up more visual noise which causes the photograph to become grainy.
The images above have the ISOs of 200, 1600, 16000, and 25800. ISO200 is the lowest my camera does, and the image looks smooth and clean. The second image is fairly higher, yet still quite clear of grain. My camera is pretty good for that! The third and fourth images are much higher, and you can see the graininess covering the whole picture. They look more like old film photos to me. Now, I've taken all of these at the same exposure, so I did have to raise my shutter speed and narrow my aperture.
A high ISO setting, such as 6400, is useful for low light photography where you want to use a faster shutter speed without flash, but this will cause a loss of detail with the grain on the image.
It is recommended that you use the lowest possible ISO to capture your image so it is the highest quality possible.
There are ways to adapt your settings so you can lower your ISO number:
+ If you use a tripod, you can use a slower shutter speed, and so a lower ISO. This will not help with capturing moving subjects as there will be motion blur.
+ If you want a shallow depth of field, you can widen your aperture which lets in more light, and so lower your ISO.
+ If you use artificial lighting such as flash, you can lower your ISO