V-World functions in multiple ways.
First, it acts as an internet of sorts, allowing the transfer of data in various forms. You can interact with this data through various methods, such as e-sheets, computers, et cetera.
Second, users who are connected directly to V-World via the holobands can interact with each other, by way of avatars, which are digital representations of real people. Avatars enter what are essentially virtual chat rooms (think old school IRC) that allow holoband users to do many of the things a person could do in real life--chat face-to-face, touch each other (the holoband makes it feel real), exchange information, et cetera. There are also games and other entertainment options in V-World. The catch is that all of this operates on Graystone-owned computer networks, so there's a fee to use it (how this works probably doesn't matter).
Enter the hackers. Hackers have figured out a way to host their own rooms, on their own servers, and jack them into the V-World, expanding it beyond Graystone Industry's control. These hacked rooms are passworded, with various levels of security place around them, so even the Graystone folks can't penetrate them. What has happened is that the users have basically taken the holoband technology, and used it to interface with their own virtual creations/worlds/games/all that fun stuff.
Zoe, being the expert hacker she was, began experimenting with the V-World code, and with the avatar code--something easier for her since she was Daniel Graystone's daughter, and had privileged access one assumes. Eventually, Zoe managed to create not just an AI, but a self-aware and sentient AI, which, since it "lived" in V-World, she fashioned after herself. Further, Zoe was able to give the AI *personality,* which too was crafted after her own. The end result was basically a virtual/digital copy of Zoe.
After the train accident, Daniel used Zoe's software to "rip" the AI-Zoe out of V-World, and onto a flash drive. This was then uploaded into the cylon body. From then on, Zoe no longer "lived" in V-World, but rather she lives in the real world, in the body of the cylon. Whenever she wants to go into V-World, she has to interface with the holoband like anyone else (it seems she might be able to access V-World through online computers, too).
Comlicating things further, we have Daniel using Zoe's software to create a Tamara AI as well. However, the Tamara AI doesn't have the months and months of acclimation Zoe's AI had, so she doesn't understand much of anything. She's still sentient and self-aware, and has all the personality and memories of the real Tamara (debatable point, since while Daniel worked on the Zoe's software, it might not be as complete as the Zoe AI). She just doesn't know she's an AI (though that is changing, obviously).
So the result is two very special instances of artifical intelligence. Zoe, who is "living" in the cylon body (and can access both the real world and V-World), and Tamara, who is "living" in V-World (and can't access the real world, but can interact with anyone who logs into V-World).
