Hazel's and Augustus's dinner together is a significant scene in the novel because of its romance and intimacy. It's not entirely free of any thoughts of cancer, since it's so perfect that Hazel can't forget it's a cancer perk and they do discuss dying and the afterlying. But even so, it's the closest thing to a normal date Hazel and Augustus have yet had. They are able to go out alone and have a romantic dinner with no other motives or concerns besides enjoying their time together. The meal is terrific, and everything is made somewhat magical by the fact that they're in Amsterdam, which is obviously novel to them both. They're also able to drink champagne for the first time. Despite the tension Hazel feels knowing that everything has been arranged because of her cancer, it's still clearly a special event.
The existentialism motif is very prominent in this section. It begins at the start of Chapter 10 with Hazel's questioning of why certain foods are considered breakfast foods. It's a tongue-in-cheek way for the motif to make an appearance, but examining and deconstructing conventions are important parts of the philosophy. The motif is hinted at directly in the names of the hotel rooms in Amsterdam. Soren Kierkegaard and Martin Heidegger, who Hazel's and Augustus's rooms are named for respectively, were prominent philosophers associated with existentialism. More serious existential thoughts and questions appear as well. When Augustus tells Hazel he loves her, he puts it in the context of knowing that oblivion is inevitable. Among existentialism's concerns was how a person can find meaning knowing that he or she may simply cease to exist upon death, and Augustus couches his love for Hazel in similar terms. In doing so he suggests that humankind's inevitable oblivion doesn't prevent his loving Hazel. It's an important point because it also indirectly hints that Hazel's inevitable death doesn't prevent Augustus from loving her either. The existential questions continue during their dinner at Oranjee and after, as they talk about their beliefs in the afterlife and, notably, what makes a person's life meaningful. Augustus implies that one has to do something extraordinary or heroic to give life meaning, but Hazel, knowing she'll likely die without doing either, contends that value doesn't come exclusively from those sources. It's worth noting that they don't arrive at any consensus. Existentialism focused on raising these questions, but there's never been a consensus on what the answers are.
One of the novel's major themes, the realities of terminal cancer, plays a prominent role in this section as well. It appears in instances like the looks Hazel receives as she waits with her oxygen tank to board the plane, but the most notable place it shows up is Augustus's story about Caroline Mathers. August starts his story by bringing up the conventions about kids with cancer—that they fight their illness heroically and never complain, etc—and then goes on to deflate those conventions. Caroline, we learn, did not die a hero inspiring those around her to greater things. The type of brain cancer she had changed her personality, and contrary to the conventions about cancer kids, she became mean and “unpleasant,” as Augustus puts it. Augustus no longer liked her, and he stayed with her out of guilt. He didn't feel he could dump a girl who was dying. What Augustus's story makes clear is that dying of cancer, and particularly that form of brain cancer, is a slow and painful process, not just for the patient but for his or her loved ones as well. His story isn't full of hope and courage but shame and a great deal of pain.
The distinction between “Augustus” and “Gus” becomes more clearly defined in these chapters, and we learn more about his character beyond his “Augustus” persona. We see the first slight chink in Augustus’s façade of heroic masculinity and charm when he reveals that he couldn't bear to deal with people at the gate staring at them. It's an uncharacteristic move for him. Rather than use some dramatic gesture to handle the situation, he essentially hid. Another side of him comes out on the plane. He's visibly afraid when the plane begins to take off, and Hazel, in a reversal of their usual roles, has to comfort him. Once they're up in the air he can't help but show his pure excitement at the fact that they're flying without any pretense. Up until this point in the story, only Augustus’s parents have ever referred to him as Gus. Suddenly, however, Hazel begins to as well as, and she notes the difference between the two personas. She describes the emergence of “surprised and excited and innocent Gus” from “Grand Gesture Metaphorically Inclined Augustus.” It's a less guarded version of Augustus than we've ever seen, and Hazel obviously recognizes as much, and likes it, because she responds by kissing him on the cheek. This unguarded, unperformed version of Augustus remains throughout the rest of the section as he and Hazel talk about death, the afterlife, and Caroline Mathers. “Augustus” is still there, as he makes clear when he suggests he wants to do something extraordinary to make his life meaningful, but there's also a new vulnerability to him that we previously haven't seen.