Oversimplified: It’s the service that handles starting and stopping of other services, including starting them in the right order after boot. Many people hate it because of astrology and supersticion. Allegedly it’s “bloated”. But still it has become the standard on many (most?) distros, effectively replacing init.

I like init. It’s simple. I like systemd as well. It’s convenient. Beyond that i don’t have very strong feelings on the matter.

Also, see important answer by topinambour-rex.