Genocide as a word (from the Greek genos, race or tribe and the Latin -cida or -cidium, meaning "killer" or "killing," respectively), did not exist prior to 1943. It was coined by Polish-born lawyer Raphael Lemkin (1901-1959) and explained in his 1944 book Axis Rule in Occupied Europe.

At the Hague, in 1907, "war crimes" had been first defined. Lemkin felt that this particular crime did not fit the definition of a war crime. It was not a transgression of the "rules of war," but rather as a crime against humanity, itself. In 1933, he visited the Legal Council of the League of Nations in Madrid. He tried proposing that acts that he would later call "genocide" be outlawed. His proposal was not adopted.

Using the Armenian holocaust at the hands of the Turks and what was known at the time about what the Nazis had done (his documentation was primarily from 1940-1941), Lemkin formulated his concept of genocide. Unlike the rather broad way it has come to be used (pretty much any large mass slaughter or only such as that typified by Hitler's Final Solution with the Jews via the concentration camps), Lemkin felt it to be much more than the mass killing of large groups of people (related by race, ethnicity, nationality, religion, et cetera) and defined it this way:

Generally speaking, genocide does not necessarily mean the immediate destruction of a nation, except when accomplished by mass killings of all members of a nation. It is intended rather to signify a coordinated plan of different actions aiming at the destruction of essential foundations of the life of national groups, with the aim of annihilating the groups themselves. The objectives of such a plan would be disintegration of the political and social institutions, of culture, language, national feelings, religion, and the economic existence of national groups, and the destruction of the personal security, liberty, health, dignity, and even the lives of the individuals belonging to such groups. Genocide is directed against the national group as an entity, and the actions involved are directed against individuals, not in their individual capacity, but as members of the national group.
He also felt that
Genocide has two phases: one, destruction of the national pattern of the oppressed group: the other, the imposition of the national pattern of the oppressor. This imposition, in turn, may be made upon the oppressed population which is allowed to remain, or upon the territory alone, after removal of the population and the colonization of the area by the oppressor’s own nationals.
In the book, Lemkin listed several ways through which the Nazis had implemented this: political, social, cultural, economic, biological (actions that decreased the birth rate), physical (which included racial discrimination in feeding, endangering health through deprivation of medicine and shelter as well as deliberate overcrowding and unsanitary living conditions, and mass killing), religious, and moral (diverting the people's thought from moral thinking by creating an environment that encourages the more base instincts).

He recommended that there be international law against such things and was able to encourage the United Nations in 1948 to enact the United Nations Convention on the Prevention and Punishment of Genocide. It followed Lemkin's basic model defining it:

In the present Convention, genocide means any of the following acts committed to destroy, in whole or part, a national, ethnical, racial or religious group, as such:

  1. Killing members of the group;
  2. Causing serious bodily or mental harm to members of the group;
  3. Deliberately inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part;
  4. Imposing measures intended to prevent births within the group
  5. Forcibly transferring children of the group to another group.
The convention passed 55-0 and would become international law after the twentieth country ratified it, which happened in 1950. Interestingly, the United States resisted ratification until 1988, feeling that it would compromise its sovereignty, and then only with what was referred to as "reservations" and "understandings. These basically say that the United States will cede authority to the International Court of Justice, but only when it decides. When and how the Convention may be applied to itself will be determined by the United States. (To be fair, some other countries concur with some of the "reservations and understandings.")

(Sources: various websites. The relevant chapter material from Lemkin's book and the text of the Convention are also available online; quotes from there.)