General Assembly Resolution 260A (III) Article II of the Convention on the Prevention of Genocide defines "genocide" in the following manner:
In the present Convention, genocide means any of the following acts committed with intent to destroy, in whole or in part, a national, ethnical, racial or religious group, as such:
(a) Killing members of the group;
(b) Causing serious bodily or mental harm to members of the group;
(c) Deliberately inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part;
(d) Imposing measures intended to prevent births within the group;
(e) Forcibly transferring children of the group to another group
The Holocaust in Germany is the genocide familiar to most people, and it was after the Holocaust that the term "genocide" was first coined and later accepted into international law. There have been cases of genocide in Bosnia-Herzegovina, Darfur, Sudan, and Rwanda. There have also been historical events that may have met this legal definition of genocide if it had been around; these include massacres in Armenia and the atrocities against Native Americans in the United States.
See the United States Holocaust Memorial Museum's web site for a fuller discussion of the origin of the term "genocide" and how it is currently applied.