The first program that is run by the kernel.
By default it is found on the root filesystem.
Absolute minimal example: http://superuser.com/a/991733/128124
https://github.com/ivandavidov/minimal uses it to call the /sbin/init from BusyBox. Modifications that worked there:
/initcontaining just#!/bin/sh\nexec /bin/sh, although that only has one TTY
The file can be set with a kernel command line parameter init: http://stackoverflow.com/questions/20744200/how-the-init-process-is-started-in-linux-kernel