News feeds allow you to see when websites have added new content. You can get the latest headlines in one place, as soon as its published, without having to visit the websites you have taken the feed from.
You need to subscribe to a news feed in order to begin receiving headlines. To do this you need to click on the orange RSS icon that appears on a site: most web browsers will usually allow you to add the feed to your bookmarks (or favourites). Clicking on the bookmark or favourite will show you the headlines from that site.
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