Moiré is a form of aliasing caused by under sampling which forms a ripple like interference pattern.
The problem occurs because printing images and scanning images both cause loss of fine scale data. When an image is printed the image is reproduced by creating a series of coloured dots, which from a distance appear to recreate the image. When an image is scanned the scanner takes a number of tiny slices of the image and uses these to recreate the final image. Moiré occurs because the positioning of the printed image's dots differs from the positioning of the slices taken by the scanner which means that the resulting image will not contain enough of the original image to be an accurate copy and a blotchy wave like pattern of distortion will appear.
The easiest way to deal with moiré is to enable "descreen" when scanning. This causes the scanner to compensate for the loss of information. The one problem with this is that there is still some loss of information and the resulting image will not be quite as sharp as the original.
If you have an image you have obtained from the internet which sufferers from moiré there are a number of steps you can take to help correct the image. For this you will need some form of image editing software capable of applying various filters. Once the image has been loaded try a series of filters such as Gaussian Blur, Remove Noise/Dust/Scratches and Despeckle, you can also use the blur tool on particularly bad areas. The resulting images will perhaps not be perfect but will probably show great improvement.
You can view some examples below.