What does this statement about saving battery power on iOS mean? While reading the iOS 14 guide by Apple here, on page 78, In the Quit and reopen an app section

What does the highlighted statement mean?

Is it that on iOS, the apps don’t close(terminate processes is what I mean here) at all and are still active and the app switcher is just for the ease of multitasking.
Is it that the services(eg. in the mail app, the service to fetch mails and send notifications) are still on, but the app is terminated.
It is actually neither of the two. It is a third variant, namely that ordinary apps cannot run in the background. So when you're looking at some app, other apps in the background aren't consuming CPU time (which translates into battery power) - so quitting the app won't make it consume less.
In regarding to receiving notifications, which you mentioned, they will be received no matter if the app is quit or not. In some cases more battery power will actually be used here if you quit the app instead of leaving it be.
In general you should not be quitting apps unless you're experiencing some kind of bug or problem with the app where it doesn't work.