There are several gradations, since you can run a 32-bit or mixed operating system on a 64-bit-capable CPU. See http://unix.stackexchange.com/questions/134391/64-bit-kernel-but-all-32-bit-elf-executable-running-processes-how-is-this/134394#13439464-bit kernel, but all 32-bit ELF executable running processes, how is this? for a detailed discussion (written for x86, but most of it applies to arm as well).
You can find the processor model in
/proc/cpuinfo. For example:
$ cat /proc/cpuinfo Processor : ARMv7 Processor rev 10 (v7l)
ARMv7 (and below) is 32-bit. ARMv8 introduces the 64-bit instruction set.
If you want to see whether your system supports 64-bit binaries, check the kernel architecture:
$ uname -m armv7l
On a 64-bit processor, you'd see
armv8 (or above).
Right now, if you were running a 64-bit ARM, you'd know.