It is accurate, if uncharitable, to describe the Dwarven language as "the sound one makes when gargling a mouthful of pebbles suspended in a pint of phlegm." Gutteral and frequently monosyllabic, at face value it appears to be a tongue ideally suited for manual laborers who dislike conversation and prefer to express themselves through a series of grunts, harrumphs and growls. While this summation is indeed technically true, it misses the driving force behind all dwarven endeavors: concision.
To a dwarf, perfection is achieved only when there is nothing superfluous left to be taken away, and this philosophy is reflected in everything they do, be it engineering, art, or language. Just as they do not believe in needless ornamentation, neither do they believe in talking more than is necessary. The shorter and more concise the sentence, the closer it is to perfection. Density of information and efficiency of transmission is merely a happy byproduct of this philosophy, but it is one that dwarves are happy to utilize as if gives them a decided advantage both at the forge and in battle.
Such concision carries over into their written language as well, which uses ideograms instead of an alphabet. While this provides similar information density -- in the space most races need to write a word, dwarven can contain an entire sentence -- it makes learning to read and write the language much harder than learning to speak it. Written Dwarven is extremely angular system (imagine Chinese inscribed with a chisel) and is slow to adopt new words, for each ideogram must be specially crafted by a master smith and then approved by a council of elders. This process can take centuries.
Fortunately, where Dwarven truly excels is in the expression of numbers and formula. Their mathematical systems are superior to those of any other race, and are the easiest to understand and use (compare Roman vs. Arabic numbers as an example.)
Dwarven is rich with deep throaty sounds, and many core concepts such as "help me," "I am injured," or "I love you" can be communicated with little to no motion of the jaw. (There is an Elven joke about an old dwarf king who, while sitting on his throne, had a severe coughing fit. His subjects nodded grimly, drew their weapons, and cut each other's heads off.) Properly spoken Dwarven sounds like a mixture of Russian, German, and Hebrew, and when translated into Common their clan names are typically translated as "Copperbeard" or "Stoneaxe." Due to their close-knit communities and belief in family before individual, dwarves always list their family name before their given one.
The dwarven preference for concision exists even in naming and honorifics and the shorter the title the most exalted it is.* A family member, or one who is deeply impressed by another dwarf, would refer to him with a shorter (and therefore loftier) title, suggesting that in the speaker's mind the dwarf is without flaw. Conversely, using a longer title than is warranted is insulting as it suggests the addition of unnecessary decoration.
Now imagine a dwarf talking to an elf, who are well-known for their flowery prose. Not only was the creation of ambassador races a necessity, but this long-standing tradition of "words seen as insults and terseness as high praise" goes a long way to explain the dwarven reputation for irritability and surliness.
*This is reflected most accurately in the dwarven title Smith. No word has ever been as misunderstood, as it is not a true translation of the "smith" concept as used in elven, orc or draconic. In the Dwarven language, a Smith is most accurately translated as "someone who can expertly shape materials". To be considered a Smith you must have mastered not only what is traditionally considered smithing, but also three or four other craftsman disciplines as well.
The title of Smith, because of its simple perfection, indicates a lofty ideal. Lesser titles are more wordy, as they require more specific words. For example, a blacksmith is one who can only shape the metals, but a Smith can shape that and more.
To other races, dwarves seem obsessed with smithing, basically giving the title of Smith to all of their highest officials. What they fail to recognize is that the Smith in charge of the temple might only be average at blacksmithing, but he is a master of dwarven politics. To dwarves, shaping truth and life is also a form of smithing, and not that different from shaping gems or metals.
The only title higher that Smith is "Shaper" (one who can shape all things), but that is a title too lofty for a mortal, and is reserved for those dwarves of legend who designed and formed Pellatarrum in the Engines of Creation millennia ago.