Usually software functionality is built up in layers, the lowest being the “drivers” which interact with the hardware, then the operating system, which marshals the drivers into consistent infrastructure services, then the middleware which ensures communication and interaction among various functions, and so forth up to the presentation layer which interacts with humans. This layering implies that a given function is dependent on a “stack” of capabilities within the machine; the stacks for many functions are partially shared, and it is difficult to separate out one of them for easy distribution.
Recent advances in virtualisation – in great part driven by the Open Source movement, have made it possible to separate out individual functional stacks and create independent packages, similar in function to a washing machine or a toaster: hence the term “appliance” used in this context.
Appliances are much more movable than traditional stacks, and in particular lend themselves quite readily to the demands of Cloud computing.