Systemd (a suite of system management daemons) replaces the init scripts of Debian Wheezy that we all saw running at every boot, giving us a slightly faster boot time and not so much on screen during the boot.
It may be a great advancement in Debian/Linux evolution, but it seems to have been thrown into Debian Jessie without any warning. There are many voices against its implementation, its default addition to Debian, and that it was passed by vote more than by principle (Debian's do one thing and do it well - i.e the individual scripts running daemons for each purpose).
There is a forked Debian now, called Devuan, that seeks to provide repositories with packages independent of systemd. Installing Devuan will setup the apt files that will prevent systemd-sysv installing (hence systemd from controlling startup).
Debian should still run on the init system, if we want it to.... but probably not for long...
You need to start the system in single user mode (press e on a line of the grub menu, add single, enter), or run a Live CD and chroot to your system, to remove systemd-sysv
(not systemd) and reinstall sysvinit
You might need to chroot
if there's no grub menu (to start in single user mode), or if you tried to remove systemd from a normally booted system and it left the system unbootable (as /sbin/init remains a link made by systemd but systemd is now removed).
install the SysV init packages and remove systemd-sysv
systemd-sysv with a '-' after it means it will uninstall
faq's from debian users
Note: that I initially removed "systemd" and I couldn't get past a grub rescue on boot, so I had to re-install systemd... but removing systemd-sysv is enough.
Prevent apt from installing systemd-sysv packages in the future.
this is the file that Devuan installs to apt preferences.d.
Actually this method does not prevent APT installing a package - as when there is no alternative it will install low pinned packages anyway!! The best way is to install a dummy package that conflicts with the package that should not be installed ever - but where that is for systemd-sysv I know not.
also read here on running svinit even with systemd installed
After removing systemd (which you're not meant to do) and installing sysvinit, my GRUB installation pooped - on reboot it came to Grub rescue. chrooting and updating grub had no result. When I used Boot Repair, from the Live CD, it took a long while to look at the GRUB install and then got me to clean it off and re-install it.
Chrooting from a Live CD
1st mount the system partition you want to change to the root of, then chroot into it
see my chroot page
and in the case of re-installing svinit, run the install/remove commands above
exit and unmount