The Political Climate of the 14th Century
To fully understand exactly what brought about the changes in the art of war in Europe over the course of the 1300s, it's important to start from the beginning. The 1400s was a time of great changes in how things were done, across the board.
People were learning very quickly that the feudal system that had been the core of Medieval society for so long was simply not working anymore.
The biggest problem lay in the fact that as Kings and Lords handed out fiefs to the knights who pledged loyalty to them, those knights left the land to their children - generally, divided between them.
This overcomplicated things to such a degree it became near impossible to tell exactly who really owed fealty to whom. Never mind the fact that most fief-holders were only obligated to forty days of service, which completely eliminated the possibility of long term military campaigns, even when they could figure out who they actually owed service to.
As a result of this confusion, and the inability to straighten it out, the idea of professional soldiers began to come into play. Men who were paid to serve continuously, including pike men and archers, as well as cannoneers.
Edward III was the one who took the idea of contracting soldiers to the point it remained at for a long time to come: contracts were written out in such a way that the indentured man in question would agree, for a set length of time, to serve under the King for a wage agreed upon by both, and he would bring with him a certain number of men. Though the idea started in England, it did eventually spread to the continent, and was a strong factor in the Hundred Years War.
While there were complications to this method (most notably, the formation of mercenary companies which often demanded to be paid off in order to leave a region alone), none could deny that it worked far better than the fealty system.
With the formation of much larger armies came the need to outfit those armies more effectively. With the increasing use of crossbows and cannons, it became necessary to strengthen the defenses the men wore.
The climate of warfare rampant in the 1300s - including the Hundred Years War between England and France, and the Great Schism, which caused no less than three popes to exist simultaneously at one point, to name only two - led to changes in battle plans and in equipment.
The days of the Feudal Knight had ended.
The new warrior was the mercenary soldier.