You should leave those there.
The local loopback connection is for your Avast AV. Think of the local loopback as the network inside your PC that is used by different pieces of software to inter-communicate (before the tech-nuts jump up and down, I realise this is not the best or probably most accurate definition of a local loopback, but a very high level, laymans definition).
The other network connection is the connection between you and your router.
Hope this helps,