Khan has clearly read and enjoyed Moby Dick. With his dying breath he directly quotes from the novel.
Ahab/Khan: From hell's heart, I stab at thee; for hate's sake, I spit my last
breath at thee."
Earlier in the film he intentionally misquotes a couple of different lines;
Khan: "I'll chase him round the Moons of Nibia and round the Antares
maelstrom, and round perdition's flames before I give him up!"
Ahab: "I'll chase him round Good Hope, and round the Horn, and round the
Norway maelstrom, and round perdition's flames before I give him up!"
Ahab: He tasks me; he heaps me; I see in him outrageous strength, with an
inscrutable malice sinewing it
Khan: He tasks me, he tasks me, and I shall have him
As to the significance thematically, it's reasonably clear that Khan sees himself cast in the role of Ahab, chasing his white whale, Kirk. Ironically he meets much the same sticky end, substituting his lust for vengeance with the conduct of a good captain and leader.
Wikipedia notes that the film's director stated (in an audio commentary) that they intentionally added a copy of the book and lingered the camera over it in order to make the parallel clear to the viewing audience.
Khan's pursuit of Kirk is central to the film's theme of vengeance,
and The Wrath of Khan deliberately borrows heavily from Herman
Melville's Moby-Dick. To make the parallels clear to viewers, Meyer
added a visible copy of Moby-Dick to Khan's dwelling.
For a scholarly review of the other parallels in the film (some strong, others substantially more tenuous) you can read.
The Wrath of Ahab; or, Herman Melville Meets Gene Roddenberry by Elizabeth Jane Wall Hinds