From the source (official) blog, about the new version 126.96.36.199:
The Twitter app for Windows Phone 8.1 is receiving a nice update today that adds a couple of new features. With this update, you can now use Cortana to launch a new Tweet in the Twitter app by saying something like “Cortana, Twitter new Tweet I love Twitter”. You can also now share websites from Internet Explorer on your Windows Phone to the Twitter app.
The changelog in the Windows Phone Store is wrong as I write this, so ignore it...
In addition to what's mentioned in the quote, the under the hood addition to the 'Share to' list also means that Twitter now pops up in the People hub again, as one of the accounts that can be linked. So Twitter updates, once signed in, can appear in the relevant pane there.
Some partial screen proof of the new Twitter in action:
I couldn't get the Cortana integration working here - maybe that's region-specific (e.g. USA?) Comments welcome.