When you do something in a way that expresses how very sad or mournful you feel, you do it woefully. You can also use this adverb for things that are done really badly, like your woefully sloppy cake decorations.
If you sigh woefully, "I miss my friend who moved away," you're speaking in a voice full of sorrow and longing. And if you graduate from high school not knowing how to speak even rudimentary Spanish, you can say that you are woefully lacking in foreign language skills. The "sorrowfully" meaning is the older of the two, but the "terribly" meaning is slightly more common. Woefully and woe are rooted in the Old English lamentation wa!