If the name Cortana sounds familiar, you're obviously a fan of classic Xbox FPS Halo - in the game, she was an advanced AI which acted as faithful personal assistant to the lead character Master Chief. Microsoft clearly intends for the WinPho8.1 version to fulfil much the same role, though presumably without helping you get all kill-happy.
The service will be heavily linked to Microsoft's Bing search engine and will be fully voice-controllable. You'll be able to use it for standard tasks such as setting calendar entries, but more impressively, it will learn about your habits, tastes and contacts, and understand natural language. Introducing the service, Microsoft's Joe Belfiore gave the example of telling Cortana to "remind me to ask my sister about her puppy next time I speak to her"; Cortana worked out instantly who his sister was and set a reminder that would flash up next time he called her.
Chief to this working properly will be the Notebook feature in which Cortana will store information about your interests, the people who matter to you and what your daily habits are. As she learns more about you, Cortana will add entries to the Notebook, which you'll be able to approve or otherwise. If she comes to the conclusion that your wife is someone important to you, for instance, she'll add her to your 'Inner circle'. If you don't correct that information, she might make the decision to put a call from your wife through to you even if it comes in during your designated 'quiet hours'.
So in short, Cortana will meld Siri-like talents with Google Now-style capabilities, but judging by the demonstration given by Belfiore, she looks twice as clever as the pair of them put together. We're interested to see how smart she is in the real world.