Federico Viticci, MacStories:
Version 3.7 of Dropbox, available now on the App Store, adds an action extension that lets you copy any file that can be shared with iOS’ native share menu directly to your Dropbox account. The extension is fairly basic: you can save to your root Dropbox folder and navigate sub-folders; when uploading, a modal dialog will show a progress bar, which will be automatically dismissed when the upload is done...
Because the action extension is available anywhere on iOS with share sheets, Dropbox has essentially created a universal “Save to Dropbox” feature, embedded natively in iOS and that developers get “for free” by supporting extensions.
It's nice to finally have iOS 8 function added to Dropbox.