I don't know what Avast is doing there (I do not use any AntiVirus app, as I see no benefit from it). But as to the second part of your question: You should not really need to explicitly close an app, as Android normally does a good job taking care itself. For details, please see the Process LifeCycle description as described on the Android developers page -- for a short look, see this graphical description:
Image taken from BottomLessInc Blog
You can see three arrows going from the "Paused" state: Directly to "destroyed" (explicitly "closed" the app), or via "Stopped" -- and back to "Running". In simple words: When you "leave" the app in the background and afterwards return to it, it goes back to "Running". If you don't return, and the system decides it is no longer needed. "Destroyed" you can take as "ended and cleared from memory", "Paused" as a kind of "Stand-By for immediate access", and "Stopped" like "Ready to be cleaned up".
Again, this is a very simplified explanation. If you need more details, the "big keyword" for this is "OOM Killer" (OOM = Out Of Memory), which is the part of the system taking care you won't run out of ressources. See e.g. this blog article for more details.