ISO stands for "International Organisation of Standardisation" which is the name for the body that standardises ratings for camera sensors. It comes from the Greek word isos which means equal.
ISO measures the sensitivity of the image sensor. The lower the number the less sensitive your sensor is to light and the finer the grain.
A higher number means your sensor becomes more light sensitive and allows you to use your camera in darker situations. The cost of doing so is more grain.
To demonstrate this better below is a selection of images all taken in natural light with an aperture set to f4 and shutter speed of 1/8 second. Note how the ISO adjustment increases the light in the exposure of each image.
This image was taken at ISO 16000, I have zoomed in on part of the image so that you can clearly see the grain and poor quality.
Compare it to this image taken in the same lighting but at ISO 100. No grain and much better quality.
I recommend keeping your ISO down as low as circumstances will allow. In general most DLSR Cameras can cope with ISO settings up to 1600 without introducing too much unwanted grain.