I see a question about this on Windows.
" When you put the computer into a hybrid sleep state, it writes out all its RAM to the hard drive (just like a hibernate), and then goes into a low power state that keeps RAM refreshed (just like sleep)."
As far as I understand it joins the advantages of hibernation (saves RAM data on disk and can restore it even in case of power cut) and of sleep/suspend (fast return to full operation).
Is it the same in Linux?
UPDATE after comment:
When I say Hybrid-Sleep I am referring to a circumstance where I wanted to make my elementary OS Loki, Ubuntu 16.04-based system to sleep/suspend instead of shutting down in case of battery critical level. More here. As that setting is administered by a tool called Upower (and not by gsettings as some time before) the only options available were Shut-down, Hibernate and HybridSleep. The latter was not available until I have created a swap space (see answer under link above). Now it works and looks very similar to sleep, while the need for a swap space makes it similar to hibernation.
On the other hand:
Before setting the swap space the commands
systemctl hybrid-sleep and
systemctl hibernate gave an error message. Now,
systemctl hybrid-sleep puts the computer to sleep (which I trusted is hybrid sleep), but
systemctl hibernate shuts down the system completely instead of hibernating it, that is: when I start it back the system is logged off and all open programs are closed (no RAM data saved/restored). This makes me think that maybe hibernation and swapping RAM data to hard disk don't work on my hardware and, although swap space is needed to use the option 'HybridSleep' in Upower settings, what happens on my system is not really Hybrid-Sleep, but just Sleep.