To be woebegone is to be sad, forlorn, or heartbroken. The woebegone expression on your face tells everyone how totally bummed out you are.
The word woebegone doesn't make its meaning clear at first glance: it seems to imply that woe, or extreme sadness, is gone. This adjective actually stems from a Middle English phrase, wo begon, "beset or surrounded by woe." So if you see your friend looking upset or glum, you might want to ask, "Why so woebegone?"