The adverb awfully has two drastically different meanings. Literally, it means in an awful manner. For example, we might say that a football player who had a bad day on the field played awfully. But the word also has a more slangy sense, making it synonymous with very. For example, we might say that a player who scored three goals played awfully well. This usage might be considered out of place in formal writing, and it can cause confusion.
The latter sense came about in the middle 19th century and is British in origin. The more literal sense is of course many centuries old—as old as the adjective awful, which has been in English many centuries.