A family of processor architectures used in many embedded applications, network and other appliances, and almost all smartphones.
ARM is a family of processor architectures especially used in low-power devices. It is commonly found in many embedded applications in consumer and industrial products, in network appliances, in almost all smartphones and tablets, and in some servers.
ARM (the company) designs the instruction set and logical architecture. The physical architecture, as well as companion processors and boot code, is made by system-on-a-chip (SoC) vendors.