Would you please explain ayah 92 of surah an-Nisa'? 

Allah said, interpretation of meaning: It is not for a believer to kill a believer except by mistake. If he kills a believer by mistake, a believing salve must be freed, and blood money must be paid to the victim's family unless they remit it. If the victim belonged to your enemy and he was a believer, a believing slave must be freed. If the victim belonged to people, with whom you have a treaty, blood money must be paid to his family and a believing slave must be freed.  If he does not find that, he must fast for two consecutive months to seek repentance from Allah. Allah is ever All-Knowing, All-Wise.

In the Name of Allah, Ar-Rahmaan, Ar-Raheem.

All praise is due to Allah, and peace and blessing be upon the Messenger of Allah, his household, his companions, and his followers.

This ayah talks about unintentional killing and its rules, and it mentions three cases. It starts by mentioning that it is unlikely that a believer kills a believer except by mistake (It is not for a believer to kill a believer except by mistake.). This is the only possibility according to Islamic perspective, since it is hard to imagine that a Muslim can kill his Muslim brother intentionally. Moreover, there is no circumstance in this life, which can weaken the relationship between two Muslim brothers to the extent that one of them kills the other intentionally.

If he kills a believer by mistake, a believing slave must be freed, and blood money must be paid to the victim's family unless they remit it.

The first case: the killing is committed against a believer whose family is Muslim, and lives in a Muslim country. In this case, two things must be done: a) Freeing a believing slave in order to compensate the Muslim society for killing a believing soul by reviving another believing soul and such is the case regarding freeing slaves according to Islamic perspective. b) Paying diyah (blood money) to the victim's family, in order to calm down their agitated souls, and compensate them for losing some of the victim's usefulness. However, Islam recommends that the victim's family should pardon the killer, if they are convinced that doing so is correct, since pardoning is more conducive to atmosphere of sympathy and tolerance inside  Muslim society.

If the victim belonged to your enemy and he was a believer, a believing slave must be freed.

The second case: The killing is committed against a believer whose family is non-Muslim, and belongs to a country, which is in state of war against Muslims. In this case, a believing slave must be freed in order to compensate for that believing soul, which was killed, but it is not allowed to pay blood money to his people, who are in state of war against Muslims so in turn they use it to fight Muslims. Furthermore, there is no place for seeking to please the victim's family since they are in state of war against Muslims and enemies of Muslims. 

If the victim belonged to people, with whom you have a treaty, blood money must be paid to his family and a believing slave must be freed. 

The third case: Killing is committed against a believer whose people have a treaty with Muslims, a treaty of peace, or a treaty of thimmah (permitting non-Muslim to live in a Muslim state). In this case, a believing slave must be freed, and blood money must be paid to his family, who has a peace treaty with the Muslims, because their peace treaty with the Muslims entails the protection of their blood, like the blood of Muslims.

 In this case, the ayah did not mention that the victim was a believer, and this led some commentators of the Qur'an and jurists to deduce that the text was unqualified  , i.e. the ruling is to free a believing slave, and pay blood money to the victim's family (ally of Muslims), even if the victim was  not a believer. Such interpretation should be examined, since the reference at the beginning of the ayah was about killing a believer, (It is not for a believer to kill a believer except by mistake.). However, their interpretation is possible. Finally, if one is unable to do the prescribed kafaarah (expiation), the diyah (blood money) is to fast for two consecutive months in order to seek repentance from Allah. Allah knows best.