Kamakura period was the golden age of the sword making. Many valuable swords now exist were made during Kamakura period. The war between Genii family and Hei-shi family at the late Heian period demanded more swords and more sword smiths.
After the Gen-pei(源平) war, the results of many precious live experiences led to improving in sword making techniques. Also, the emperor Gotoba encouraged sword making and treated sword smiths very highly. As a result, they created large numbers of the valuable swords during Kamakura period.
The style of the swords during this period varies considerably, we usually divide into three stages; early Kamakura period, middle Kamakura period, late Kamakura period.
The Kamakura period was called Kamakura period because the center of the political power which is Kamakura Bakufu(鎌倉幕府) was established at Kamakura area by Minamoto-no-Yoritomo(源頼朝). He was a head of the Genji.
At the end of the Heian period, Genji(源氏) attacked Hei-shi(平氏) but failed. As a result, a direct line of Genji, Minamoto-no-Yoritomo(源頼朝) was sent to Izu(considered far away then). There, he met Hojo Masako(北条政子) who was a daughter of a small local official, Hojo family. Eventually, Minamoto-no-Yoritomo overthrew Hei-shi family with the help of his wife Masako and her father, Hojo Tokimasa.
At the end of the Heian period, Hei-shi family was the top of the society. It was said, “if you are not a part of Hei-shi family, you are not a human being”. A society like that created too many enemies. Yoritomo raised an army, attacked Hei-shi family, and won the war, that end Heian period. The power of the Kamakura government(鎌倉幕府) spread all over Japan.
Yet the imperial court and aristocrats still existed in Kyoto. Kamakura Bakufu had military, police and political power. The imperial court was the department of public administration. Thus those two big rivals controlled the country in the different field and kept the balance between them.