Lower ISO will produce better overall image quality, but it will require a longer shutter speed or larger lens apertures, which themselves reduce the image sharpness. Higher ISO will allow more lights in, resulted in brighter photo, which increased the amount of noise on the photo. Selecting the right ISO sensitivity is a matter of deciding on the sensitivity that provides the right combination of image noise, shutter speed and aperture.
I took some photo with Nikon D40X with different ISO so you could see the clear different.
ISO 100
Image is sharp and pretty dark.
ISO 200
Image still look sharp, slightly brighter than ISO 100.
ISO 400
Still looks good.
ISO 800
Image is bright, but notice that there are extra white dots, which is the noise.
ISO 1600
Image are much brighter with more noise.
ISO 3200
At 3200, it is very much exposed, but with the high noise level.