The term "culture of impunity" refers to a situation in which people in a society have come to believe that they can do whatever they want with impunity (which means without having to face any consequences for their actions). In the context of a genocide, it means that the culture of the country was such that people literally felt that they could get away with murder.
This concept is pretty much 180 degrees opposed to the idea of the rule of law. The rule of law is the idea that all people will be punished if (and only if) they break the law. There is no impunity for anyone under the rule of law.
My colleague above did a great job in explaining what a culture of impunity is, as opposed to a culture respectful of the rule of law.
During the Rwandan genocide of 1994, at least a million Tutsis were massacred by the majority Hutus in the space of about three months (April-June 1994). The genocide ended when the Tutsi rebel group, the Rwandan Patriotic Front (RFP), defeated the regime of President Habyarimana, a Hutu. The President's plane was shot down on April 6, 1994, and the genocide began almost immediately after the incident.
How did the culture of impunity lead to the massacre of millions of Tutsis and moderate Hutus who would not support the majority agenda?
1) State sanctioned propaganda against the minority Tutsis.
The Hutu majority clung to power desperately. Therefore, the Hutu-led government allowed propaganda that marginalized Tutsis to prevail as part of the national discourse.
2) State sanctioned convictions and subsequent arbitrary executions of Tutsis from between 1990-1993.
Reports of these 'rehearsals' for the actual genocide confirm that prior to April 1994, Tutsis were already systematically persecuted and subjected to relentless violence at the hands of loyal Hutu revolutionaries. All of these acts were sanctioned and supported with military might by President Habyarimana's government. During his despotic reign, no Hutus were ever punished for violent attacks on Tutsis. Indeed, 'legislations of impunity' were enacted by Habyarimana's government for the purposes of protecting Hutus from prosecution.
3) Racial superiority theories championed by the majority Tutsis.
Prior to majority rule by the Hutus, the Tutsis, who were originally Cushite cattle herding warriors, had ruled Rwanda for hundreds of years. The Tutsis had more caucasoid features than their fellow Hutus. As such, this fact was further exploited by the British imperialist forces in Rwanda.
A British Army officer, John Hanning Speke, introduced the 'Hamitic theory.' The Hamitic theory basically states that those who owe their light skin to European ancestry had greater right to rule and to domination over other peoples (notably darker-skinned peoples). So, the Tutsi reign engineered much resentment among the Hutu people. When the situation was reversed, the Hutu majorities sought to 'right past wrongs' by systematic eradication of the Tutsi race.
4) A wholly inadequate justice system.
Out of some 600 magistrates, only 1 in 50 held law degrees during Habyarimana's reign. Those who held judicial positions exercised authority at the discretion of the ruling government. It was clear that Tutsis were never going to receive any sort of justice from such a corrupt system. To make matters worse, there was no independent bar system; therefore, the government decided who represented the defense, a travesty of justice. This clearly fostered the culture of impunity you mentioned. The rule of law was clearly non-existent in this virulent atmosphere.