i'm not sure about attempting to convince someone that they should like it, but i can talk of why i like the book so well. such a thing is so subjective. for me it's all about how the language affects the reader, what holds or doesn't hold a reader's attention, what appeals or doesn't appeal to any given reader.
Apocalypse Now was my first introduction to Conrad. the film was realeased 5 days before my 21st birthday, in august of 1979, only 4 years after the fall of saigon. i had been watching that war on television for most of my life.
i have a clear and vivid memory of going to see that movie. the theater was filled with vets. before the movie began many of them were greeting each other aloud and calling out their names, battalions, companies, squad names, tours of service, etc as greetings to one another. there was, in the theater, a great sense of comraderie, support, and pride. it seemed to me that we all knew we were there to see something that hadn't been seen before.
my father had told me that the film was based on a Conrad story so i was aware that there was a book, but had never read it.
after the film ended we all, and i do mean all, sat there, watching the credits roll, in silence. no one got up to leave. no one spoke. seriously, no one left until the credits were over and the screen went dark.
i did not see the movie again nor read the book until much later.
i did see the chronicle of the production
Hearts of Darkness: A Filmmaker's Apocalypse when it came out. and finally, sometime in the mid 1990's saw the movie for a second time.
i read
Heart of Darkness for the first time sometime around 2005 or 2006 i think. for a class called Important Literature of the 19th Century.
i was VERY taken with the language. Conrad was Polish, fluent in French, and wrote in English. much of his writing reflects this, for me, in a positive way. his style is very painterly, bordering sometimes on decorative.
(if he'd written hard-boiled detective fiction he'd be raymond chandler who is also one of my favorites.

)
i connect with his narrative style. the language is very poetic to me and
draws me in. (this happens every time i read the book, not just the
first time.) Conrad is very adept at making me "feel" the mood of the
scenes.
in the class we also discussed the structure of the story.
a frame tale told by an unnamed narrator who tells the story
of marlow telling the story, which i loved. it creates a remove
from the narrative, a question of "reliability" of the narrator.
can we believe the narrator is telling the story of marlow telling
the story accurately or is it, as are most second and third hand
stories, colored by the narrator's memory of marlow whose experiences
and memories are also colored by subsequent life experiences and the
passage of time.
these are two of the reasons i love the story. the language and the
structure.
i'm not even going to start on themes and motifs in this post.
i've blathered enough. heh.