Why does Marlow long to meet Kurtz so badly in the novella Heart of Darkness?
This question is a fairly complex one, and is one to which even Marlowe himself cannot supply a definite answer until the end of the second section of the novella. Only when Marlow fears that Kurtz is dead immediately following the native attack on the steamboat does he realize that he wishes to have "a talk with Kurtz." A careful reading of Marlow's subsequent narrative will reveal that Marlow is looking for either an affirmation of his hopes about mankind or a confirmation regarding his worst fears about humanity.
In other words, Marlow feels that he will meet one of two possible men in Kurtz. The first possibility is that Kurtz turns out to be the "remarkable" humanitarian that many of Marlow's acquaintances in the Company describe him as. If this characterization turns out to be true, humankind in the form of Kurtz is affirmed as a higher order of animal that is able to overcome natural environments, urges, etc. However, the second possibility for Marlow is that Kurtz is a changed man, one who once was the symbol of civilization but who now has turned to baser instincts and uncivilized practices. If this Kurtz turns out to be real, Marlow's fears about human nature are confirmed. Those fears center on Marlow's "suspicion of [the African natives and Europeans living and working in the Congo] not being inhuman."
Regardless of the actual man Kurtz turns out to be, Marlow is driven to meet Kurtz by a personal need to satisfy his own curiosity and clarify all the ambiguity concerning Kurtz that has been mentioned throughout the first two sections of the novel.