In the 70's and early 80's:
- RAM was very very expensive
- it ran at the same speed as the CPU.
- programming by hand in assembly language was common
So - simplifying very much here - it made sense to design CPUs where each instruction performed a lot of work, was easy to translate from high-level languages, and where programs were expected to use memory as a scratchpad, as opposed to internal CPU registers. This makes the CPU design complicated and power-hungry.
The RISC principle advocates making instructions simple and lightweight, recognizes that compilers are the ones usually generating assembly language and not humans, and provides lots of registers (faster than RAM) for use of intermediate calculations. This makes the CPU design simpler and requires less power. The assembly language is more complicated and you usually need more instructions to do things - but as RISC was becoming prevalent, RAM prices were falling.
RISC looked like it was going to win out in the late 80's/early 90's, but Intel started putting RISC-like features into it's CISC-like CPUs - and moved forward with additional performance features such as caching, branch prediction, register renaming, etc., and today's 64-bit CPUs from Intel and AMD can be considered a hybrid.
However, ARM CPUs:
- are still much more simpler internally.
- ARM licenses its CPU core to chipset manufactuers. So it's easy for companies such as Qualcomm or Apple to integrate a CPU core into a phone chipset.
- the above two contribute to power savings which are very important on mobile devices, even though they do not perform as well as Intel hardware.