This is the "duduk" (DOO-dook); it's name comes from a Turkish word for "pipe." It is played in Armenia for social and cultural events, usually with one duduk player making a drone sound and another playing a melody.
It is an ancient instrument, known to be used in Armenia at least since the reign of Armenia's king "Tigram the Great," 95 - 55 BC.
Its distinct sound has been sought for use in some Western films-- the sound of Mr. Timnus playing his "flute" in The Chronicles of Narnia, The Lion. the Witch and the Wardrobe was created with a duduk.
The sound of the duduk has been compared to sounds of the oboe, clarinet, and saxophone. But really, it doesn't mimic any of these-- because the sound it makes can only be made by the duduk.
Would you like to hear it?
Here is a lovely duet composition with duduk and guitar, played in this Youtube video by Vigen Hovsepyan and Vahan Ghalechyan: