The director actually says that they're not using dedicated servers, so there won't be world tendency. Remember, with Demon's Souls, you had to login to a fixed dedicated network hosted by the publisher when playing the game online. This is what is apparently not returning. But all the other network features of the game are still there. You will occasionally see other players moving around, dying, the messages left by other players, etc. There will still be co-op and PvP elements, just like in Demon's Souls. Presumably all these features will now be handled via PSN and XBL itself, instead of through a dedicated separate framework. This also means that PS3 and 360 players will not be able to play with each other.
There are a bit more details about the new online elements too, since the full interview is out. He says that there are two specific areas which are new to the online mode of Dark Souls. One aspect is that you will be able to share your playing experience with friends, and so as you play the game and tackle the various harsh challenges, you won't feel that you're doing it alone, but rather that you have other friends who are also facing the same challenges. This sounds to me like a social networking system built into the game, and might be related to the campfire teaser they showed in the announcement trailer.
The other aspect he mentions is that there will be some sort of mutual roleplaying aspect in the game where each player's game will interact with other players in some way, to extend the roleplaying aspect. It's unclear to me what this actually means at all, and I'm not even sure if it's a good translation of what he's trying to say because of how vague it is. But basically it sounds like the game will feature a lot more interaction in non-direct methods, just like the original game but expanded in ways the team felt would enhance the experience further.