Eulogies are a bleak topic, no doubt about it. But since Augustus has the will to tackle them, we sure have to.
As his health deteriorates and he prepares for death, Augustus asks his loved ones (in this case Hazel and Isaac) to write eulogies so he can hear them while he still has some time left. Why is he so concerned about his eulogies? Well, in a way, it's as though cancer has robbed him of his heroic story. He wanted an obituary that would paint him as special and heroic, but he feels like he'll just be another premature death.
Through the eulogies, Augustus is able to hear and shape the way that he's remembered. He listens to them and—get this—even offers suggestions. (Isaac isn't too keen on that: "and then finally, he said, "Goddamn it, Augustus, editing your own eulogy" [20.54].)
Augustus may not have control over whether he lives or dies, but now he knows his legacy. And with the loving and kind eulogies that his friends and loved ones give him, it's clear that he has left his mark, even if it's not exactly what he thought it would be.
Hazel already has a eulogy prepared, right? So why doesn't she give it at Augustus's funeral? Well, her original eulogy served to offer Augustus some comfort and validation about how much he meant to her; but now it's Augustus's parents who need the comfort:
I went on spouting bullshit Encouragements as Gus's parents, arm in arm, hugged each other and nodded at every word. Funerals, I had decided, are for the living. (22.20)
Classic Hazel, always looking out for those around her.