إِنَّ الَّذِينَ تَوَلَّوْاْ مِنكُمْ {Indeed, those of you who turned back}: Those are who fled from the battle and descended from the mountain, who wanted this world instead of the Hereafter.

إِنَّمَا اسْتَزَلَّهُمُ الشَّيْطَانُ بِبَعْضِ مَا كَسَبُواْ {it was Satan who caused them to slip because of some [blame] they had earned}: In fact, Satan has no authority over humans, but when a person falls into a misstep, Satan sees him weak, so take the chance to whisper to him if this person neglects the remembrance of Allah (swt). In another verse:

وَقَالَ الشَّيْطَانُ لَمَّا قُضِيَ الأَمْرُ إِنَّ اللّهَ وَعَدَكُمْ وَعْدَ الْحَقِّ وَوَعَدتُّكُمْ فَأَخْلَفْتُكُمْ وَمَا كَانَ لِيَ عَلَيْكُم مِّن سُلْطَانٍ إِلاَّ أَن دَعَوْتُكُمْ فَاسْتَجَبْتُمْ لِي فَلاَ تَلُومُونِي وَلُومُواْ أَنفُسَكُم مَّا أَنَاْ بِمُصْرِخِكُمْ وَمَا أَنتُمْ بِمُصْرِخِيَّ إِنِّي كَفَرْتُ بِمَآ أَشْرَكْتُمُونِ مِن قَبْلُ إِنَّ الظَّالِمِينَ لَهُمْ عَذَابٌ أَلِيمٌ

{And Satan will say when the matter has been concluded, “Indeed, Allah had promised you the promise of truth. And I promised you, but I betrayed you. But I had no authority over you except that I invited you, and you responded to me. So do not blame me; but blame yourselves. I cannot be called to your aid, nor can you be called to my aid. Indeed, I deny your association of me [with Allah] before. Indeed, for the wrongdoers is a painful punishment.”} (Ibrahim: 22)

So no one should use Satan as an excuse for himself, rather he should use the excuse that he made a mistake.

إِنَّمَا اسْتَزَلَّهُمُ الشَّيْطَانُ بِبَعْضِ مَا كَسَبُواْ {it was Satan who caused them to slip because of some [blame] they had earned.}: Because of their behaviours, Satan came to them and led them to their doing.

وَلَقَدْ عَفَا اللّهُ عَنْهُمْ {But Allah has already forgiven them}: Allah (swt) has pardoned them, and repentance is hoped for the cessation of wrongdoing. The largest reform movement in society is called repentance, when a person repents, he decides not to go back to what he has done of everything bad. Islam always calls for all the elements of goodness, this is why the door of repentance is opened.

إِنَّ اللّهَ غَفُورٌ حَلِيمٌ {Allah is Forgiving and Forbearing.}: Allah (swt) forgives but here by his Forbearing; Allah (swt) is merciful to this person when he falls into a stumble. So that when the archers violated the commands and looked forward the spoils, Allah (swt) forgave them by his Forbearing.