When computer users think of the buzzword "64-bit", usually the first thing that comes to mind is the Windows operating system, which comes in two flavors; 32-bit or 64-bit. Like a computer, a smartphone or tablet also has an operating system, (usually Android OS, iOS, or Windows), and to run as 64-bit, it needs a processor that is built to do so.
Up until very recently, processors in mobile devices have all been 32-bit, as have the operating systems. However, technology market research firm ABIresearch has predicted that sales of 64-bit mobile devices will exceed 1.15 billion shipped in 2018, representing a 55% market share, so this is technology that is coming fast.
The majority of smartphones and tablets run a 32-bit OS, partly due to there not being 64-bit microarchitecture to run it on in most devices. After all, the first 64-bit mobile processor and OS (Apple's A7 and iOS) only showed up about 6 months ago, in September 2013. Even for devices that feature a 64-bit processor, Windows 8.1 has only just gotten support for 64-bit Bay Trail mobile processors (though the Surface 2 Pro could run 64-bit Windows 8.1 via an Intel i5 processor, which isn't actually a mobile-optimized chip).