I think this is one of those features that Apple should have explained a lot better, because it is very confusing in its current state. I have to admit that I still don't know whether I should turn it off or not and which benefits it gives to me on a per-app basis. As I understood it, this feature allows apps to do certain tasks in the background (e.g. fetching content) when the OS thinks that I might be needing the app soon (it supposedly records usage patterns and predicts when you an update will be required). It's not actually opening the app or letting it run in the background, so no realtime multitasking, it just allows it to do a certain kind of task at a specific time.
This makes perfect sense for apps that need to fetch new data whenever you open them, like news or social-media apps, but less with other apps, in my opinion. 1Password barely benefits from this unless you are changing your entries very often. It will almost always be sufficient to let the app update its database once you actually use the app again, you won't really notice it.
I recently discovered that this feature is also tied to push triggers which are incredibly useful for messaging apps. When you receive a push notification on, say, WhatsApp, the push trigger will update WhatsApp in the background at the same time, saving you that little delay when you open the app and have to wait till the message is loaded.