systemd is a collection of daemons, libraries and tools for system management. Ubuntu's Upstart system was replaced with systemd starting with Ubuntu 15.04.
systemd is intended to make the boot process faster and more efficient when compared with pre-existing init systems, such as by using parallelization.
More detailed technical information about systemd can be found on the Ubuntu Wiki and Wikipedia. Freedesktop.org also has a page for systemd.
Lennart Poettering, the author of systemd, has a blog post providing background on why systemd is needed, including some history on other init systems such as Upstart.
systemd is still considered controversial by some; many of these reasons are listed on without-systemd.org. Lennart Poettering also wrote a blog post in defense of systemd. Regardless, many major Linux distributions are switching to it. This includes Ubuntu since its parent distribution, Debian, is one of them. Ubuntu now uses systemd by default starting with Ubuntu 15.04.
