By 1944 when kamikaze planes began to be used the Japanese defence ring had fallen apart and the Japanese began to understand that the only way out of the war was to inflict as many casualties upon the Americans as possible, in vain hope that the American public would grow war weary and force their government to sue for peace. This was the motivation shins the Kamikaze.

Now to understand why a pilot would be willing to sacrifice themselves on a suicide mission, you have to understand Japanese warrior culture. The Japanese samurai code of Bushido was considered important and every military personal would have known it. The code stresses loyalty unto death, it also stressed that to die in battle, in service to the emperor was the greatest honour a young man could bring to his family. To preform a successful kamikaze attack would bring great honour to your family, which was extremely important in Japanese society. To refuse to die in service of the emperor would have brought great shame and dishonour onto your house. Japan was a highly militarized society, so military acts were also looked upon with great respect and admiration.

That's what motivated the kamikaze, the idea that there death would serve the emperor and bring great honour to their family.

Source:

Japan's imperial army it's rise and fall by Edward drea

A history of japan by L.M Cullen

This letter was written by a pilot named Isao Matsuo to his parents in May 1945. I have written this out from the book 'World War II: The Autobiography' by Jon E. Lewis. It's a great collection of sources and I'd recommend it to anyone wanting to know personal stories about the war from civilians and soldiers alike.

I have bolded several lines that I think refer to your initial question on what motivated these pilots.

Dear Parents:

Please congratulate me. I have been given a splendid opportunity to die. This is my last day. The destiny of our homeland hinges on the decisive battle* in the seas to the south where I shall fall like a blossom from a radiant cherry tree.

I shall be a shield for His Majesty and die cleanly along with my squadron leader and other friends. I wish that I could be born seven times, each time to smite the enemy.

How I appreciate this chance to die like a man! I am grateful from the depths of my heart to the parents who have reared me with their constant prayers and tender love. And I am grateful as well to my squadron leader and superior officers who have looked after me as if I were their own son and given me such careful training.

Thank you, my parents, for the twenty-three years during which you have cared for me and inspired me. I hope that my present deed will in some way repay what you have done for me. Think well of me and know that your Isao died for our country. This is my last wish, and there is nothing else that I desire.

I shall return in spirit and look forward to your visit at the Yasukuni Shrine. Please take good care of yourselves.

How glorious is the Special Attack Corps' Giretsu Unit whose Suisei bombers will attack the enemy. Movie camera-men have been here to take our pictures. It is possible you may see us in newsreels at the theatre.

We are sixteen warriors manning the bombers. May our death by as sudden and clean as the shattering of crystal. Written at Manila on the eve of our sortie.

Isao.

Soaring into the sky of the southern seas, it is our glorious mission to dies as the shields of His Majesty. Cherry blossoms glisten as they open and fall.

*This is most likely referring to the battle of Okinawa, which took place from April-June 1945 and resulted in the US occupation of Japan.

Whilst it is true that not every kamikaze pilot chose this path voluntarily, Isao's letter is a good example of the overall mindset of the pilots.

Due to the eventual superiority in the east of Allied troops and the fact that the war for the Japanese was going very poorly it soon become a fight for survival, both for the nation and for the Emperor - which, at the time, were almost one in the same.

Warband's comment above is clear as to the reasons why kamikaze developed and how the traditional concept of Bushido (which itself was instilled by the nationalist government, much the counterpart of the Nazis' Volkisch revival movement).

Kamikaze was itself a pretty well organised tactic - it wasn't a free-for-all suicide attack, but pilots were taught in their manuals not to waste their lives freely and to only attack if there was a target that was within reach. This shows that, whilst the tactic itself was born out of desperation of a failing war, it was still a military and therefore honourable act.

However, some pilots do not see the glory of the attacks as much as Isao. To turn their backs on such a task would be considered dishonourable (and I believe some pilots were stigmatised after the war for not following through on their missions) despite their wishes. This is shown by a line from the letter of Ichizo Hayashi -

To be honest, I cannot say that the wish to die for the emperor is genuine, coming from my heart. However, it is decided for me that I die for the emperor.

This shows that he believes his destiny/duty is to engage in the mission despite not being so willing to die for his emperor as Isao.

We must also remember that we only have a handful of letters regarding kamikaze pilots, and they may not have poured their true emotions into it for fear of dishonouring themselves and their family.

So to answer your question, what motivated the kamikaze pilots? A failing war, nationalist duty and the code of honour that has been a part of Japanese society for many centuries.

NINJA EDIT (ninjas seem appropriate): http://www.theguardian.com/world/2002/aug/22/japan.historybooks This is some extracts of the manual given to the pilots.