If "service manager" doesn't ring a bell, think of it as a "manager of background tasks/applications". Some applications which only run in the background as background processes are called "services" (sometimes also called "daemons" or simply "servers"), and systemd offers ways to create/start/stop/restart/manage/introspect those, as well as configure how and when they start, what permissions they have when starting, and things like that. It basically replaced very old tools like "inetd".

The other main part of systemd is that it's an init system, which means that it's meant to be started as the very first process (PID 1) by the kernel during startup, and it then launches all the other processes/services which need to run before you even get to log in. Compared to the old sysv-init system which systemd basically replaced, systemd is faster and much more featureful and modern.

systemd also has a lot of other more optional components (it's a big bundle of system tools, altogether). Whether these are used is up to the administrator or the distribution which might preconfigure them (or not).

As usual in the open source world, there are alternatives for everything. You don't technically need to use systemd, or you could just use some of systemd's components and not others, but its main components are the default for most distributions nowadays. Some more niche distros pride themselves in not using systemd at all. But systemd is great overall (there's a reason why most distros use it).