When you've shared a web page you're reading on your iPad with your Facebook friends, or zapped out an iPhone snapshot via iMessage, your first tap has probably been that little square button with the upward-pointing arrow.
That's the Action button, and it comes in handy whenever you want to share, print, save, or otherwise interact with something on your iPhone or iPad—anything from a photo or a "Note," to a PDF or a click-worthy article.
Even better, you can also choose which sharing and "actionable" buttons you want to appear front and center. Not interested in, say, Reading List (Apple's lackluster answer to Instapaper)? You can easily tuck the "Add to Reading List" button in the Action pane out of sight. Rather share web pages on Tumblr than Facebook? No problem. Wish there were an easier way to fax documents (yes, some people still prefer faxing) using a third-party app? You might be able to add an Action button for that.