You may ask, what is this Nationalism of which you speak? We'll let Bishop Cauchon explain: "I can express it only by such phrases as France for the French, England for the English, Italy for the Italians, Spain for the Spanish, and so forth" (4.120).
This may not seem like such a radical idea today, but back then it was crazy talk. During Joan's time, people that mostly spoke French and lived in a land referred to as France didn't necessarily call themselves French. If you zoomed back in time and asked your average French speaking peasant where they came from, they might say Normandy or Aquitaine, but never France. The land was divided among lots of smaller duchies and fiefs. People were more loyal to their feudal lord than the king. In Shaw's play we see Joan burst onto the scene with a new philosophy. She thinks that all these people going around speaking French ought to be united under a strong French king.
Joan comes to symbolize this new Nationalism, and as a result she terrifies the feudal lords, French and English alike. The Earl of Warwick will elucidate us as to why: "Men cannot serve two masters. If this cant of serving their country once takes hold of them, goodbye to the authority of their feudal lords" (4.19). He goes on to say, " If the people's thoughts and hearts were turned to the king, and their lords became only the king's servants in their eyes, the king could break us across his knee one by one; and then what should we be but liveried courtiers in his halls?" (4.112).
This is exactly what happens in the future. If you want a good example, watch Henry VIII on The Tudors; you'll see the absolute power that future monarchs hold. Eventually the feudal lords become exactly what Warwick describes, only the king's servants. When Warwick orchestrates Joan's execution, in his mind, he's burning a symbol of this new Nationalism that threatens his power.
Note: It should be recognized that Shaw's use of the word Nationalism, is anachronistic, meaning that it is out of place in this time period. The term didn't come into use for several centuries after Joan's death. Shaw says in his preface that he chose to do this to better help modern audiences understand the play.