Hi, current Stanford ESS student here. I just was in your shoes a year ago, so hopefully my comments are helpful.
First of all, relax. They're not interviewing you as much as you should be interviewing them. At this point, your POI likes you and you both should be focusing in off it's a good fit for both of you or not. Come prepared with questions. But again, relax.
Depending on if you put down multiple faculty with whom you are interested in working with on the application, you might rotate chatting with your POI1 and POI2 ...(through POI #N I guess). I was only interested in my PI, so that time I was cycling through the lab group.
The Department will send you an itinerary soon, if they haven't already. This will include morning breakfast with other potential students and the department chair and other people, and then from there you will probably go on your "interviews" with faculty. But it really depends on your POI after this point--mine had a chat with me and the other interested students, and then cycled us through the lab members. Remember that they are trying to figure out if you are going to be a good fit too (and vice versa). I think the itinerary includes some free time, and then in the evening there's a dinner for all the potential students with current grad students so you all can ask the good questions (are they happy? How boring are department seminars? Is the cost of living in Palo Alto making them live under bridges? etc etc etc). There will be free food and drinks.
Relax, and good luck!