SystemD is a system manager. Also known as an initialization system, or a sort of system manager of systems, if you will.
With regards to Ubuntu - which I am most familiar with in the Linux world - SystemD debuted in Ubuntu 15.04 (an off-cycle release). Prior to this, such as Ubuntu 14.04 and 14.10, a different manager called Upstart was utilized. Upstart had previously replaced the venerable SystemV (also known as SysV). Ubuntu 16.04 supports all three to some extent (SystemD, Upstart, and SysV) by attempting to convert what it perceives as Upstart and SysV calls to SystemD calls. Only one init system can be in use at one time, and in Ubuntu versions 15.04 and later, it's SystemD. Beginning with Ubuntu 17.10, only SystemD init calls should be utilized (17.10 purportedly dropped support for the Upstart init daemon).
The scripts and examples on this site were written on Ubuntu 16.04, unless otherwise indicated. They should function on 18.04 as well, but may not work on versions prior to 15.04, such as 14.04.
Personally, I make a point to wait at least a year after a long-term Ubuntu release before I begin to adopt it and learn its nuances. This allows time for major bugs to get worked out. Ubuntu long-term releases are supported for 5 years, so this isn't a big deal for me personnally. As of this writing in August 2019, I'm still using 16.04.x versions exclusively, but have begun experimenting with 18.04 on a test system. If you happen to still be using any version prior to 16.04, I encourage you to upgrade. SystemD adoption is a good reason for that, in-and-of-itself. As mentioned above, the old Upstart and SysV init processes still work in 16.04. If you have old scripts that use them you'll be fine until you want to upgrade to 18.x or later Ubuntu versions.