Durzagh is the dragon language spoken in the Pamirs and the Karakoram, as for example by Arkady and his band. Temeraire first heard about it and started learning it from Tharkay, who understood it and spoke it well enough to be understood, although there are sounds in Durzagh that humans can not make. The voices of dragons mimic human voices more easily than the reverse.
Temeraire was pleased to learn that dragons have their own language, as he expected that this would make it all the more obvious to the British government that they are intelligent. However, Tharkay warned him, somewhat sarcastically, that the British were more likely to think dragons to be unintelligent "for speaking a tongue other than English."
When feral dragons from the Pamirs began to be drafted into the British Aerial Corps, it was necessary for some of the younger officers who had some skill with languages to learn Durzagh, the native tongue of these dragons. Only Celestials and perhaps Imperials retain the ability to learn new languages for more than a few weeks after hatching, so the ferals could not be taught English.
Durzagh is related to languages spoken by dragons in other parts of the world. While carrying the King and Queen of Prussia to Posen, in what is now Poland, Temeraire met a band of feral dragons who spoke a language that sounded "a little bit like Durzagh in places, but... was too different to make out, at least when they spoke so quickly."
Later on, Temeraire discovered that the language of the dragons in southern Africa also had "many bits which are like Durzagh." This similarity helped him to communicate with these dragons when he, Lily and Dulcia were trying to locate their captains and crews, who had been taken captive by Kefentse and brought to Mosi-oa-Tunya.