Action Extensions have been around since iOS 8 (see here for some further reading). They allow apps like ours to interact with others. In the context of Papers, the action extension that we have built allows you to import webpages and documents from other applications like Safari or another PDF reader. Actually just about anywhere you see the share icon
When you tap the share icon in another app you'll see two or three rows of icons. The last row in grey are your action extension.
If you do not see the "Add to Papers" icon, scroll to the right and tap on the "More" button.