Because of his skills, everyone has been looking at Jack as if he were the leader, and it's pretty clear that is a role he can manage, but doesn't want to accept. At its core, 'White Rabbit' is the episode where Jack finally gives into the inevitable, and takes the role of leader. Of course, since this is Lost, there's a lot more to it.
Jack has been burning the candle at both ends since the plane crash (and, as we find out in this episode, for quite some time before that) and now it begins to take its toll. In the opening sequence, one of the survivors goes swimming, and Boone, the lifeguard, tries to save her, but nearly drowns himself. Jack dives in, pulls him back to shore, then goes back--- but it's too late. Jack takes this very personally, even though he didn't know this woman at all. Scarcely has he begun to deal with this problem, when another crisis emerges--- the water supply is starting to run low. Everyone's looking to Jack, and then things get worse--- he sees the man in the suit in the woods. Only it's not just a man in a suit--- it's his father.
Jack obviously doubts his sanity, but nevertheless goes chasing after the phantom. But he becomes so obsessed that he ends up chasing it over a cliff, which would have killed him--- if not for the appearance of Locke.
The two men have their first real conversation, where Jack reveals that he's chasing a ghost. Locke then tells him what he knows --- that the island is different. The others don't want to talk about it, but they all instinctually know it. Locke is convinced that this is happening to Jack for a reason--- mainly as a test to prove to himself that he can lead.
A note: Locke says that he has "looked into the eyes of this island and what I saw was beautiful." What he doesn't consider is that it might be beautiful to him, the paralyzed man who can now walk, but it not might be for Jack. Perhaps the island is testing Jack somehow, and what we will come to realize is that while he can accept his role as leader, he can not quite buy what Locke is selling. This is a fundamental difference between the men, which will end up being a huge part of the drama of the show.
For the first time, we get a good look at the kind of man Jack was pre-island, and more importantly the relationship that he had with his father. Jack's father, like him, was a surgeon, and it's clearly suggested that their relationship was not a good one. The entire reason Jack went to Australia was to find his father, who was the midst of something unexplained (we'll find out what, but not from Jack) Eventually, he drank himself to death. Jack was accompanying his father's body back to the States, and it's clear from the last flashback, that he was hoping that he could finally end their tormented relationship. How ironic, that even though Jack eventually finds the coffin which carried his father, his body is gone. Now he can never lay it to rest.
(Another mystery: The coffin was shut, but the body wasn't in it. What happened? I would like to float the possibility that somehow the island is using Jack's father in some way. Over the past few years, several of the characters are revealed to have been involved with Jack's father, and because of that importance, the island took it, and I believe at some point in the shows final seasons, we will understand that purpose.)
Perhaps one reason the body was used was to lead Jack to a cave with freshwater spring. Jack also finds scattered parts of the plane and the coffin. This leads to him finally accepting, however reluctantly, his role as leader. When he brings the water back, he tells them that it is time for the others to start preparing for the possibility that rescue will not come, and that if "they can't live together, they're going to die alone" However, not everybody will take Jack's word as gospel, and that's going to lead to problems.
Jack is so front and center during this episode, everyone seems to fade into the background a bit. But we do get some more information. One of the more prominent characters is Claire. During the episode, she faints from lack of water, which leads to another crisis, when the already diminishing water is mysteriously taken. This sets up another sweet moment between her and Charlie. Claire knows that everyone thinks of her as a potential time bomb--- how long dot hey have before this new problem develops--- but Charlie is one of the only people who doesn't seem scared by this. There is definitely something between them, but Claire doesn't know Charlie's demon yet.
Boone seems to be trying to prove himself. He demonstrated that when he tried to save the woman that drowned, and he clearly blamed Jack for coming back with him. Then when Jack disappears, Boone tries to use the water to help Claire, arguing weakly that someone had to step up. A mini-mob begins forming, which is dissipated by the return of Jack. Boone isn't happy about this either.
Sawyer seems to be setting himself up the unofficial black market of this island. This becomes clear when he tries to bargain with Shannon over the price of some insect spray. When the water disappears, he's the obvious scapegoat, which becomes more suspicious when Sun mysteriously shows up with water. He reveals that he traded the water for a fish Jin caught --- that must have been fun for both of them--- but not before Kate tries to force it out of him, something which clearly delights him. Sun and her husband are clearly getting worried about their crisis, but their approaches are different--- she wants to try and communicate with the others to try and find leadership, he says that he will provide for her--- hence the trade with Sawyer. There is also a moment where Sayed tries to interrogate Sun, and replies to Kate's intervention with the reply that she understands what he's saying. Perhaps Sayed has insight into this from personal experience, and it turns out, he knows what he's talking about.
Kate seems to be taking on the role of a miniature enforcer--- she doesn't seem to want to lead, but she seems drawn to authority figures like Jack, Locke and Sayed. This is particular ironic considering her flashback, but there is clearly compassion in her behavior. Locke is assuming the role of half survivalist (he gathers water from the moisture on the leaves) part mystical yogi. When he goes into the woods after Jack, he assures Kate he knows how to find him, and there he is. The obvious answer to this is that he tracked Jack, but what if there was another way? Did the island guide him like it seemed to guide Jack?
The episode ends with Jack telling Kate why he was on the plane, but not why he went on his search in the first place. Maybe it's because he has trust issues or (more likely) he doesn't want to admit that what he saw was real. But this is a critical episode for Jack, and it demonstrates (if there was doubt before) that Matthew Fox is the right actor to be at the center of Lost Few people could demonstrate being strength and fear in the same character, but, as he demonstrated on Party of Five, Fox knows how to do it. The hallucination doesn't appear for awhile, but Jack still has real ghosts, and they're going to be biting at him on the island over and over.