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.