If you look inside /proc/sys/fs/binfmt_misc, you’ll probably see a file named qemu-arm or something similar, with contents along the lines of
enabled
interpreter /usr/bin/qemu-arm-static
flags: OCF
offset 0
magic 7f454c4601010100000000000000000002002800
mask ffffffffffffff00fffffffffffffffffeffffff
This instructs the kernel to “interpret” binaries matching the given magic value using /usr/bin/qemu-arm-static. This allows it to use QEMU to emulate ARM CPUs (and fix up system calls to match the ARM ABI) and run ARM binaries transparently on any system where QEMU can emulate ARM CPUs, including your 64-bit x86 PC.
In your case, since the ARM binary is statically linked, no additional setup is required. Dynamically-linked binaries need their native libraries to be available too.
On Debian-based systems, including Ubuntu-based systems, this is set up by the qemu-user-static and binfmt-support packages: the qemu-user-static package registers the binfmt_misc configurations that QEMU can handle using update-binfmts, and the binfmt-support package ensures that the registered configurations are loaded into the kernel (binfmt_misc is a kernel module).
See also What types of executable files exist on Linux?, What kinds of executable formats do the files under /proc/sys/fs/binfmt_misc/ allow?, and How is Mono magical?