The Hundred Years' War was a conflict between France and England which lasted from 1337 to 1453. The war had three distinct phases: Edwardian, Caroline, and Lancastrian. Such a long war is difficult to summarize in just a few words, but the war essentially originated as a succession crisis.
There were no heirs to the French throne; Edward III of England tried to claim the throne, but the French nobility rejected him. Eventually, this conflict spiraled into war between France and England. Edward gained control of the English Channel, and the Treaty of Brétigny in 1360 ended the Edwardian phase. England gained a large amount of territory.
However, the tide soon turned against England. Charles V of France began rebuilding the French navy after he ascended to the throne in 1364. He resumed the war (hence this period is called the Caroline phase) and reclaimed a large amount of territory for France despite doing his best to avoid open conflict with England. The Caroline portion of the war ended in 1389 with the Treaty of Leulinghem.
The next period of the Hundred Years' War is called the Lancastrian War. The English King Henry V attacked France in 1415, winning a number of battles (most notably the Battle of Agincourt) and capturing most of northern France. The 1420 Treaty of Troyes ended the war by creating a marriage alliance between England and France which would allow Henry's heirs to inherit the French throne.
However, the Hundred Years' War was not over. Many French nobles opposed the Treaty of Troyes and tried to continue the war. Henry VI responded by invading France and laying siege to Orleans, but Joan of Arc helped rebuff the English advance.
Hampered by poor leadership and internal strife, the English began to falter in their war against France. Eventually, the internal conflicts became so great that Henry VI ceased fighting the war for the French throne to focus on domestic affairs in England.