What is death according to Buddhism? When does it occur? Why do so many people die simultaneously in natural calamities? What did Buddha say about death? Please give references of Buddha's teachings.
What is death acoording to Buddhism? Here is one definition
Death and the impermanence of life
In the teaching of the Buddha, all of us will pass away eventually as a part in the natural process of birth, old-age and death and that we should always keep in mind the impermanence of life. The life that we all cherish and wish to hold on.
To Buddhism, however, death is not the end of life, it is merely the end of the body we inhabit in this life, but our spirit will still remain and seek out through the need of attachment, attachment to a new body and new life. Where they will be born is a result of the past and the accumulation of positive and negative action, and the resultant karma (cause and effect) is a result of ones past actions.
This would lead to the person to be reborn in one of 6 realms which are; heaven, human beings, Asura, hungry ghost, animal and hell. Realms, according to the severity of ones karmic actions, Buddhists believe however, none of these places are permanent and one does not remain in any place indefinitely. So we can say that in Buddhism, life does not end, merely goes on in other forms that are the result of accumulated karma. Buddhism is a belief that emphasizes the impermanence of lives, including all those beyond the present life. With this in mind we should not fear death as it will lead to rebirth.
The question about when death occurs is even more important, because to a practitioner of Buddhism, death is not an eventuality that will arrive someday. Death and meeting death is part of our daily practice of meditation. We don't think of the body dying but day by day we face and face again the temporal nature of life and ask ourselves if we are making the most of life for spiritual advancement by learning to come to terms with death.
Here is an illustrative story from a PBS special on Buddhism http://www.pbs.org/wgbh/pages/frontline/shows/tibet/understand/dying.html
An example of this attitude can be found in the bioraphy of Milarepa, who began his meditative practice after having killed a number of people through black magic. The realization of his impending death and the sufferings he would experience in his next lifetime prompted him to find a lama who could show him a way to avert his fate. His concern with death was so great that when he was medititing in a cave his tattered clothes fell apart, but he decided not to mend them, saying, "If I were to die this evening, it would be wiser to meditate than to do this useless sewing."1
This attitude epitomizes the ideal for a Buddhist practitioner, according to many teachers. Atisha is said to have told his students that for a person who is unaware of death, meditation has little power, but a person who is mindful of death and impermanence progresses steadily and makes the most of every precious moment. A famous saying of the school he founded, the Kadampa, holds that if one does not meditate on death in the morning, the whole morning is wasted, if one does not meditate on death at noon, the afternoon is wasted, and if one does not meditate on death at night, the evening is wasted.
Here are a couple quotes attributed to the Buddha that imply what Buddha thought most important, cessation of suffering and Nibbana. http://www.life-changing-inspirational-quotes.com/buddha-quotes.html#Death
Buddha Quotes on Death
"Even death is not to be feared by one who has lived wisely."
"It is better to travel well than to arrive."
This trend of thinking beyond life and death continues here http://en.wikiquote.org/wiki/Gautama_Buddha
Even death is not to be feared by one who has lived wisely. As quoted in Wisdom for the Soul: Five Millennia of Prescriptions for Spiritual Healing (2006) edited by Larry Chang, p. 193 This is actually a pithy modern-day 'summary' of the "Abhaya Sutta" (AN 4.184). It appears in "Buddha’s Little Instruction Book" by Jack Kornfield (p88).
Another example that Shakyamuni Buddha reveals his lack of concern about death is under the Bodhi tree before his realization. http://en.wikiquote.org/wiki/Gautama_Buddha
Let my skin and sinews and bones dry up, together with all the flesh and blood of my body! I welcome it! But I will not move from this spot until I have attained the supreme and final wisdom. The Jatka (From the Attainment of the Buddhaship. Also is in the Nirvana Sutta.)
The essence of the Buddha's teaching is not to cling to physical existence and in the same line do not fear death. What dies is the life we conceptualize in our mind. What is untouched by death is the consciousness that the Buddha invites us to develop in our practice.
Death is unsatisfactory:
Some questions about death (or about the Tathagata) are unanswered:
So, Malunkyaputta, remember what is undeclared by me as undeclared, and what is declared by me as declared. And what is undeclared by me? 'The cosmos is eternal,' is undeclared by me. 'The cosmos is not eternal,' is undeclared by me. 'The cosmos is finite'... 'The cosmos is infinite'... 'The soul & the body are the same'... 'The soul is one thing and the body another'... 'After death a Tathagata exists'... 'After death a Tathagata does not exist'... 'After death a Tathagata both exists & does not exist'... 'After death a Tathagata neither exists nor does not exist,' is undeclared by me.
And why are they undeclared by me? Because they are not connected with the goal, are not fundamental to the holy life. They do not lead to disenchantment, dispassion, cessation, calming, direct knowledge, self-awakening, Unbinding. That's why they are undeclared by me.
And what is declared by me? 'This is stress,' is declared by me. 'This is the origination of stress,' is declared by me. 'This is the cessation of stress,' is declared by me. 'This is the path of practice leading to the cessation of stress,' is declared by me. And why are they declared by me? Because they are connected with the goal, are fundamental to the holy life. They lead to disenchantment, dispassion, cessation, calming, direct knowledge, self-awakening, Unbinding. That's why they are declared by me.
So, Malunkyaputta, remember what is undeclared by me as undeclared, and what is declared by me as declared.
People die because they are born.
I think that the purpose of Buddhism or the Buddha is not to teach what death is. I think its/his intention is to teach how to be in the face of death, how to respond to the fact/existence of death:
The latter reference describes some of the states of (the Tathagata's) death:
Then the Blessed One addressed the monks, "Now, if it's out of respect for the Teacher that you don't ask, let a friend inform a friend."
Then the Blessed One addressed the monks, "Now, then, monks, I exhort you: All fabrications are subject to decay. Bring about completion by means of heedfulness." Those were the Tathagata's last words.
Then the Blessed One entered the first jhana. Emerging from that he entered the second jhana. Emerging from that, he entered the third... the fourth jhana... the dimension of the infinitude of space... the dimension of the infinitude of consciousness... the dimension of nothingness... the dimension of neither perception nor non-perception. Emerging from that, he entered the cessation of perception & feeling.
Then Ven. Ananda said to Ven. Anuruddha, "Ven. Anuruddha, the Blessed One is totally unbound."
"No, friend Ananda. The Blessed One isn't totally unbound. He has entered the cessation of perception & feeling."
Then the Blessed One, emerging from the cessation of perception & feeling, entered the dimension of neither perception nor non-perception. Emerging from that, he entered the dimension of nothingness... the dimension of the infinitude of consciousness... the dimension of the infinitude of space... the fourth jhana... the third... the second... the first jhana. Emerging from the first jhana he entered the second... the third... the fourth jhana. Emerging from the fourth jhana, he immediately was totally Unbound.
Note that Nirvana is described as unbinding.
Ven. Yuttadhammo has made some great videos about this topic:
Here is a video called "Preparing for Death" and "Ask A Monk: What Do Buddhists Do When Someone Dies?"
Regarding mass casualties there is this video "Ask A Monk: Karma in a Holocaust". In here Ven. Yuttadhammo discusses a holocaust, a tsunami and the planes crashing into World Trade Center.