I thought it was fairly obvious that they were introducing us with a new class.

Both Yugiri and Thancred got a chance to show of their skills, and Yugiri later on promises to teach her fighting style to an organisation in Limsa. To me (and many others) this was an obvious introduction to an upcoming class. I originally expected her to come back in smaller quests for several patches before we would actually gain access to it, but it turn out that will already take place in 2.4

In the same way, Yugiri is an introduction to the new race we will be getting.
It is outright stated in the main scenario that she hides her face to avoid panic, because she looks very different from the 5 races. So she is a walking talking teaser preview of the upcoming race. All we know at the moment is that the new race will have a scaly tail, and either horn or some sort of long ears judging by her hood.

ps: I wonder how they are going to handle that scene after the new race becomes available. People are obviously going to change race -for fun or permanently- meaning that there will be plenty of Yugiri-race adventurers in Eorzea, giving her no reason to hide her face.