CISC = Complex Instruction Set Computer
RISC = Reduced Instruction Set Computer

ARM was originally "Acorn RISC Machines" - the name of a British computer maker.
These days they no longer make computers; they don't even make any chips - they just design a processor "core", which they license to lots of people to embed into their ASIC products.
A few vendors (eg, Samsung, Triscend) sell ARM microcontroller chips.

See www.arm.com