Armenians have been making wine for so long that there's serious scholarly debate whether they were the first winemakers in the world. Let's put it this way: they were pressing and fermenting grapes while my northern European ancestors were still figuring out that pointy things kill animals and long before the great Mesoamerican empires discovered the miracle of getting the nutrients out of corn.
It's no surprise, then, that when the secrets of distillation swept the globe, some of that Armenian wine turned into brandy, which, given the technology of the time, was sealed up in wooden casks to keep for later, lending it a dark color and a warm, rich, spicy taste imparted by the wood.
There used to be many brandy makers; when Armenia was joined to the Soviet Union, the Yerevan Brandy Company was given a monopoly, and its Ararat brands were the only brands of Armenian brandy for many years. There's a (probably apocryphal) story that Josef Stalin gave Winston Churchill a bottle of Armenian brandy that was so good that Churchill ordered several cases. Regardless, the fact is that “cognac” is the country's most well-known export, and it's only increased since Yerevan Brandy Company was purchased by Pernod-Ricard in 1998.
Speaking of Pernod-Ricard, the French get a little nettled when they see labels that say Cognac on bottles that don't come from Cognac, so in the interests of international harmony, the Armenian government decided pretty much unilaterally that the Armenian product would be called arbun, which is supposed to be a play on words for the Armenian word for “drunk” (which I don't buy–“drunk” in Armenian is harbats). If you call it arbun, no Armenian will have the least clue what you mean–they still call it kanyak, French hand-wringing nothwithstanding.
Drunk neat, Akhtamar (the 10-year brandy) has a softer edge than Cognac, but a much more floral, rich, herbaceous taste. This is something you can put in a snifter and serve to your guests after dinner, then make them guess what they're drinking.
If you're going to mix it (in which case you may want to buy a younger brandy), adjust the sweetness of your cocktail down a bit; for example, don't sugar the rim of a Sidecar made with Armenian brandy, and add an extra dash or two of pungent bitters to your Old Fashioned. This will account for the natural sweetness of the brandy. Don't stop there, though–with bitters on top of the meringue à la Pisco sour, it makes a wonderful sour; add it to wine to make an outstanding sangria.
Brandy is one of the next big things, now that we're at full saturation on vodka, American whiskey, and tequila. As demand rises, there'll be a renaissance in Armenian brandies; get ahead of the curve and pick up a bottle of this at Hi-Time Wine so you know what to compare the newcomers to.