systemd-suspend.service is a system service that is pulled in by suspend.target and is responsible for the actual system suspend. Similarly, systemd-hibernate.service is pulled in by hibernate.target to execute the actual hibernation. Finally, systemd-hybrid-sleep.service is pulled in by hybrid-sleep.target to execute hybrid hibernation with system suspend.
Immediately before entering system suspend and/or hibernation systemd-suspend.service (and the other mentioned units, respectively) will run all executables in /lib/systemd/system-sleep/ and pass two arguments to them. The first argument will be "pre", the second either "suspend", "hibernate", or "hybrid-sleep" depending on the chosen action. Immediately after leaving system suspend and/or hibernation the same executables are run, but the first argument is now "post". All executables in this directory are executed in parallel, and execution of the action is not continued until all executables have finished.
Note that scripts or binaries dropped in /lib/systemd/system-sleep/ are intended for local use only and should be considered hacks. If applications want to be notified of system suspend/hibernation and resume, there are much nicer interfaces available.
Note that systemd-suspend.service, systemd-hibernate.service, and systemd-hybrid-sleep.service should never be executed directly. Instead, trigger system sleep states with a command such as "systemctl suspend" or similar.
Internally, this service will echo a string like "mem" into /sys/power/state, to trigger the actual system suspend. What exactly is written where can be configured in the "[Sleep]" section of /etc/systemd/sleep.conf. See systemd-sleep.conf(5).
systemd-sleep understands the following commands:
suspend, hibernate, hybrid-sleep