A Linux operating system has a core program called a kernel, which has the job of creating and maintaining an environment where other programs can run. Other programs include the login prompt, the shell that lets you execute programs, etc. However, there is a chicken-and-the-egg problem: once the environment is running, how do you run the first program? This is solved by having the Linux kernel run a program called "init" as the first program, which manages everything else (bringing up services, executing the login prompt, etc). There are multiple versions of this "init" program with different features and idiosyncrasies -- the Debian committee voted to use one called systemd rather than some competitors. Switching versions of init requires system administrators to relearn how to do many things, so the committee spent a lot of time weighing a lot of factors before making this decision.
A group of programmers who make a popular version of Linux have decided to make their version of Linux start with a new program when the computer boots. Instead of using a program from the 80's called "System V init scripts", they have decided to switch to a new program called "systemd." Both programs have the major responsibility of starting the rest of the programs that make up Linux.
I found this explanation of systemd interesting (though more suitable for a wannabe hacker than a 5-year-old (though I suppose the two sets may not be disjoint)): http://0pointer.de/blog/projects/systemd.html
