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Additional to Jerry Coffin's first paragraph. Ie, ARM design gives lower power consumption.
The company ARM, only licenses the CPU technology. They don't make physical chips. This allows other companies to add various peripheral technologies, typically called SOC or system-on-chip. Whether the device is a tablet, a cell phone, or an in-car entertainment system. This allows chip vendors to tailor the rest of the chip to a particular application. This has additional benefits,
ARM supports SOC vendors with AMBA, allowing SOC implementers to purchase off the shelf 3rd party modules; like an Ethernet, memory and interrupt controllers. Some other CPU platforms support this, like MIPS, but MIPS is not as power conscious.
All of these are beneficial to a handheld/battery operated design. Some are just good all around. As well, ARM has a history of battery operated devices; Apple Newton, Psion Organizers. The PDA software infra-structure was leveraged by some companies to create smart phone type devices. Although, more success was had by those who re-invented the GUI for use with a smart phone.
The rise of Open source tool sets and operating systems also