I know this is a bit necro, but I've seen many people give the same answer all over the internet, and it is not correct. The following answers are taken directly from David Salo; an authority on Tolkien languages, who worked directly with the scriptwriters for both the LotR movie trilogy, and The Hobbit movie trilogy, and was responsible for expanding the vocabulary of these languages beyond Tolkien's original published works. Most importantly, ten years after LotR's release, the scriptwriter for The Hobbit approached him about the meaning of this very line, for consideration to be said again by Thorin.
The line you are referring to is:
îsh kakhfê ai-‘d-dûr-rugnul
As for its English meaning, the common answer of "I spit on your grave" is a PG version, which has unknown origins (Though it has been attributed to Andreas Fröhlich, the director of the German translation of the movie ). But, according to David Salo, that's not actually what it means.
I should add that “I spit on your grave” — taken, I think, from the title of cheap 1970s exploitation film — is something I would never come up with. It’s practically meaningless as applied to the immortal Eldar, and I doubt it would be used as a casual curse by the Dwarves, who took the treatment and entombing of the dead extremely seriously.
The short and to-the-point answer is this:
The literal meaning is therefore "May my excrement be poured upon the naked-jawed (ones)"; a meaning giving the full connotation of the words would necessarily be less literal and more expressively vicious.
Mirror that's easier to read
Originally, David Salo had no idea what it meant.
I had no idea what the line John Rhys-Davies uttered meant for over a decade. I don’t even know how it came to be filmed that way; a story that I heard was that he ad-libbed it on set, being unable to produce the line I wrote for one reason or another. But that is a second-hand or third-hand story, or worse, and if he has a different story to tell about it, it supersedes anything I have to say on the subject. What I always said when I was asked was that I assumed it was so unspeakably nasty as to be untranslatable — at least in polite company!
I didn’t even know exactly what he had said, much less its meaning. So when I finally got asked about it by the scriptwriter I had to find the scene and listen to it over and over and over again before I came up with:
[ɪʃˈkɑkʰʍi ɑɪ duˈrugnul]
Well, that may be Khuzdul, but it’s not my Khuzdul, and even includes a sound that I excluded from neo-Khuzdul — any variation of /w/. But when I heard that there was consideration of having Thorin use the same curse, I thought “Aha! Here’s a chance to deal with all of those questions, and the additional ones to come.” So I sat down and reverse-engineered (so to speak) a Khuzdul version from Rhys-Davies line, using my grammar and phonology.
What I came up with was:
îsh kakhfê ai-‘d-dûr-rugnul
I suggest you read the entire article to get the full story and context, but this piece will explain the Dwarvish punch of "naked-jawed (ones)":
Obviously it had to refer to the Elves in some way. But it had to be bitterly contemptuous, in a peculiarly Dwarvish way. It should go beyond the usual reflections on intelligence, sanity, sexuality and personal hygiene that are the backbone of so many English curses.
After quite a lot of thought (more than I like to admit to) I came up with the compound dûr-rugn. On the face of it, this isn’t much of an insult. Dûr simply means bare, naked, or uncovered, from a root √DAYARA (*√DAWARA) “strip, shave, make naked”;rugn (plural ragân) is the lower jaw (or chin). Dûr-rugnul is an adjectival form (here used substantively, preceded by the definite object marker id-) meaning “bare-chinned” or more literally “with naked (hairless) lower jaw.”
It is, Tolkien wrote, “characteristic of all Elves to be beardless” (Unfinished Tales, p. 247); but all adult Dwarves, male and female, have beards of which they are very proud. Only a very young Dwarf, or one who had suffered some tragic injury or illness, would lack a beard.
The beardlessness of Elves would therefore appear comic to the Dwarves, a sign that they were at best infantile, and would be an obvious subject of mockery; it might also suggest that they lacked the gonads (of either sex) to produce a proper beard. At any rate, to go about with a bare chin must appear to the Dwarves to be shameful, all the worse for the fact that the Elves appear unconscious of their shame, or even proud of it.