The link isn't all that informative about her, I'm afraid, but as far as I can find out the instrument she plays is the khomus (sometimes called the xomus), which is a Yakutian traditional instrument. Yakutia is now known as the Republic of Sakha and is an autonomous state within the Russian Federation. It's a part of the world I knew very little about so I was pleased to find this interesting article here.
It turns out that the khomus is by no means the only jaw harp, though. They are found in many cultures going by many different names - mouth harp, Jew's harp, Ozark harp, trump and juice harp being only some. It is one of the oldest known musical instruments and was believed to have magical properties so was - and, in some parts of the world, still is - often a part of shamanic rituals.
I found everything about them, from the sounds they produce to their appearance, fascinating. You can read more about them here and there are some lovely photos of them here if you are interested.