The information displayed in the Latest Activity Feed is a list of your unread 'alert' notifications from the current event you are in - these notifications are related to activity you have been subscribed to or have subscribed to yourself - they could be actions such as a new conversation being created, a comment being added or a document being updated. This feed is displayed here to allow you to have quick access to your most pertinent notifications, which you can interact with just by clicking on them without having to leave the page you are currently interacting with.
The Newsfeed displays all notifications of activity that you can access within your event. These notifications can be for subscribed or general activity - general activity is defined as notifications of actions that have happened in conversation areas you currently have access to, but you are not (or have not) been subscribed to. There are additional features present in your 'Newsfeed' that allow you to filter your notifications by importance (All/All Unread/Unread Alerts), and you can also mark all your event notifications as 'read' if you wish to.