ARM is a 32 bit RISC set architecture, mostly used in embedded systems, and mobile devices. ARM is used for this because of it's relative cheapness, and ruggedness, at the cost of speed. The architecture was originally conceived at Acorn Computers, the first devices were from the ARM Archimedes range.
ARM has traditionally been reserved for Embedded systems and mobile operating systems. The main reason is the slowness, which is acceptable when compared with the faster, but exponentially more expensive x86 and amd64 architectures. Most mobile operating systems support ARM, such as Android, and Windows 8.
ARM processors are found everywhere, from cars, to hard drive peripherals to routers and traffic lights. It supports all of the functions of traditional processors, at the cost of reduced speed. Most cheap consumer electronics, use ARM, and most, if not all military robots (UAVs, etc) use ARM for it's cost and ruggedness. Modified ARM processors are used as graphics processing units, notably the Project Denver, of Nvidia Technologies. Notably absent from the GPU arm list is AMD, which uses amd64 architectures.