As you might recall, one of the things that Facebook removed during its home page redesign was the live stream, which displayed your friends' Facebook activity as it occurred. Users were not happy that it disappeared - in fact, real-time updates became one of the top requests from Facebook users. And so it is back, but with a different implementation.
Facebook's live stream isn't a new tab or section of the homepage, like it once was. Instead, when friends post new content or update their status, a section right under the update bar appears that asks whether you want to show new posts. As more updates occur, the number of new posts increases until you click on it. Once clicked, these new posts will appear.
The live stream is not yet available to all users - Facebook rolls out updates in several cycles, meaning that it could be a few days until live streaming is available in your Facebook.