95% android apps think they are so important that they need to run in the background. For example, that google maps wants to track your location everywhere you go, even when you switch off tracking. If you install the FB app and instagram app, you lose like 5% of your cpu capacity (just a random number) because those apps will restart and track you even when you force close them (which apps you use, what games you play, how long you play them, which sites you browse, which browsers you use, which bank apps you have installed, the list of apps you have installed, which new apps you install, etc). This is why if you leave your android phone running overnight while you sleep, the phone battery drops many percentages even if you don't use it. You don't use it, but all the cached apps will still be running and using up battery while they track and run analytics on you.
So this option allows you android what apple does: prevent apps in the background from running. It does not intefere with the notification system, unlike the sleep option. Basically, it's deep sleep without any deep sleep drawbacks. You sleep through the night with a couple of percentage drops in battery.
The only drawback is for app developers, and those people tracking every bit of your behaviour as you use the phone. Their app running in the background can no longer monitor your behaviour and send reports back to their mothership.
With this, you can basically switch off the sleep/deep sleep function. Greenify and hiberation will be put to the pasture. It's ok to have as many apps in the background as possible, but they just stay in memory and don't use any CPU cycles. When you have sleep/deep sleep on, those cached apps can't run, and the system will judge that those apps are inactive, and may purge them from memory. In fact, people who are having problems with this probably run hiberation/sleep/deep sleep options with it, which is a bad idea.
