The Hundred Years' War
Henry V's invasion of France took place during what historians have come to term the hundred years' war. It was a period of intermitent battles and skirmishes between the English and French. Henry's claim to the French crown is a part of the complicated issues of royal inheritance, which were not entirely stable at this point. At the same time as Henry believes he has a right to the French crown, arguments were also being made in England as to who was the rightful heir of the English crown.
Henry's conquest in France was seen (by the English) as the greatest triumph of the hundred years' war. It played an important and symbolic role in English culture in Shakespeare's time.