Ayah

Word by Word
وَلَا
And (do) not
تَقۡتُلُواْ
kill
ٱلنَّفۡسَ
the soul
ٱلَّتِي
which
حَرَّمَ
Allah has forbidden
ٱللَّهُ
Allah has forbidden
إِلَّا
except
بِٱلۡحَقِّۗ
by right
وَمَن
And whoever
قُتِلَ
(is) killed
مَظۡلُومٗا
wrongfully
فَقَدۡ
verily
جَعَلۡنَا
We have made
لِوَلِيِّهِۦ
for his heir
سُلۡطَٰنٗا
an authority
فَلَا
but not
يُسۡرِف
he should exceed
فِّي
in
ٱلۡقَتۡلِۖ
the killing
إِنَّهُۥ
Indeed, he
كَانَ
is
مَنصُورٗا
helped
وَلَا
And (do) not
تَقۡتُلُواْ
kill
ٱلنَّفۡسَ
the soul
ٱلَّتِي
which
حَرَّمَ
Allah has forbidden
ٱللَّهُ
Allah has forbidden
إِلَّا
except
بِٱلۡحَقِّۗ
by right
وَمَن
And whoever
قُتِلَ
(is) killed
مَظۡلُومٗا
wrongfully
فَقَدۡ
verily
جَعَلۡنَا
We have made
لِوَلِيِّهِۦ
for his heir
سُلۡطَٰنٗا
an authority
فَلَا
but not
يُسۡرِف
he should exceed
فِّي
in
ٱلۡقَتۡلِۖ
the killing
إِنَّهُۥ
Indeed, he
كَانَ
is
مَنصُورٗا
helped
Translation

Nor take life - which Allah has made sacred - except for just cause. And if anyone is slain wrongfully, we have given his heir authority (to demand qisas or to forgive): but let him not exceed bounds in the matter of taking life; for he is helped (by the Law).
Tafsir

And do not slay the soul [whose life] God has made inviolable, except with due cause. Whoever is slain wrongfully, We have certainly given his heir, the one inheriting from him, a warrant, a sanction [to retaliate] against the slayer; but let him not commit excess, [let him not] overstep the bounds, in slaying, by slaying other than the killer [of the one slain], or by other than that [instrument] with which he [the slain] was killed; for he is supported [by the Law].
Prohibition of Unlawful Killing
Allah forbids killing with no legitimate reason.
وَلَا تَقۡتُلُواۡ النَّفۡسَ الَّتِي حَرَّمَ اللّهُ إِلاَّ بِالحَقِّ
And do not kill anyone whose killing Allah has forbidden, except for a just cause.
It was reported in the Two Sahihs that the Messenger of Allah said:
لَاا يَحِلُّ دَمُ امۡرِىءٍ مُسۡلِمٍ يَشۡهَدُ أَنۡ لَاا إِلَهَ إِلاَّ اللهُ وَأَنَّ مُحَمَّدًا رَسُولُ اللهِ إِلاَّ بِإِحۡدَى ثَلَاثٍ
النَّفۡسُ بِالنَّفۡسِ
وَالزَّانِي الۡمُحۡصَنُ
وَالتَّارِكُ لِدِينِهِ الۡمُفَارِقُ لِلۡجَمَاعَة
The blood of a Muslim who bears witness to La ilaha illallah and that Muhammad is the Messenger of Allah, is not permissible (to be shed) except in three cases:
a soul for a soul (i.e., in the case of murder),
an adulterer who is married, and
a person who leaves his religion and deserts the Jama'ah.
The following is recorded in the books of the Sunan:
لَزَوَالُ الدُّنۡيَا عِنۡدَ اللهِ أَهۡوَنُ مِنۡ قَتۡلِ مُسۡلِم
If the world were to be destroyed, it would be of less importance to Allah than the killing of a Muslim.
وَمَن قُتِلَ مَظۡلُومًا فَقَدۡ جَعَلۡنَا لِوَلِيِّهِ سُلۡطَانًا
And whoever is killed wrongfully, We have given his heir the authority.
The authority is over the killer. The heir has the choice;
if he wishes, he may have him killed in retaliation,
or he may forgive him in return for the payment of the Diyah (blood money),
or he may forgive him with no payment, as is reported in the Sunnah.
The great scholar and Imam Ibn Abbas understood from the general meaning of this Ayah that Mu`awiyah should take power, because he was the heir of `Uthman, who had been killed wrongfully, may Allah be pleased with him, and Mu`awiyah did eventually take power, as Ibn Abbas said on the basis of this Ayah. This is one of the stranger of matters.
فَلَ يُسۡرِف فِّي الۡقَتۡلِ
But let him not exceed limits in the matter of taking life.
They said:this means the heir should not go to extremes in killing the killer, such as mutilating the body or taking revenge on persons other than the killer.
إِنَّهُ كَانَ مَنۡصُورًا
Verily, he is helped.
means, the heir is helped against the killer by the Shariah and by divine decree.
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