What are wavelets and multiresolution processing in image processing?

Wavelets are used in compression of images. Certain wave forms are very good at compressing certain types and portions of images (other wave forms are better at other image types (think of a brick wall compared to the branches of a tree!) The combination of appropriate wavelets can result in great image quality and small image sizes.
MultiResolution processing (like MrSid) is a way to make a very large image (often many Gigabytes ) presentable on equipment that cannot hold all that data in memory. An illustration is to take a bunch of detailed jpeg images of a scene (many hundred or thousand) and stitch them all together. For each zoom level generate a new jpeg so that when an observer is close in they are looking at a presnentation of one of the detailed images but when zoomed out to see 16 times as much surface they are presented with a jpeg made of 16 original images (but it has been compressed so that it does not take up more memory than one original).