All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.
The cause behind which this verse was revealed is that Az-Zubair had a dispute with one of the Ansar about streamlets in the lava plain, and the Prophet said, “Water your ground, Zubair, then let the water run to your neighbour.” The Ansari said: “It is because he is your cousin.” Thereupon his face changed colour and he said: “Water your ground, Zubair, then keep back the water till it returns to the embankment, and afterwards let it run to your neighbour.” So the Prophet paid regard to az-Zubair’s right by the clear decision when the Ansari made him angry and he had given them advice which would have made matters easy for both of them. [Agreed upon].
The above verse was revealed to clarify that adhering to the judge of the Prophet (PBUH) is an obligation during his lifetime and to abide by his teachings and rulings afterward; In addition, a Muslim is obliged to be fully satisfied with them not otherwise since acting contrary will be a beginning of impending doom in this life and in the Hereafter.
In this regard, Ibn Khatheer (May Allah have mercy on his soul) stated: "In this verse, Allah, The Exalted Swears by Himself, that none will be a believer till the a Muslim is fully satisfied with the rulings and teachings of the Prophet Muhammad (PBUH) regarding all of his matters, since what he judged is the right that must be adhered to whether in secrecy or in openness, in addition of accepting them (Ruling and teachings) with the fullest conviction that’s why He, The Exalted Said (What means): "Until they make thee judge in all disputes between them, and find in their souls no resistance against Thy decisions, but accept them with the fullest conviction." It means: If they ask you (PBUH) for a judge then convicting and adhering to it in secrecy and in openness is an obligation side by side with no refusal, argument nor a delay as stated in this narration which says: "By the One in Whose hand is the soul of Muhammad, none of you [truly] believes until his desires are subservient to that which I have brought.” Kindly refer to [Tafseer Al-Quran Al-Adheem vol.2 pp. 349].
Thus, the most important ruling extracted from the former verse that adversaries are obliged to seek the ruling given by Islamic Sharia regarding any dispute, and whosoever avoid this is considered a sinner; besides, when The Exalted, Said [they can have no (real) Faith] is a sign of being a sinner not a disbeliever save if a person denied the Sharia itself or accuse it of having a defect.
Finally, a Malikee's scholar, Ibn Al-Arabi (May Allah have mercy on his soul) stated : "It was reported that the cause for which this verse was revealed is due to a dispute between one of hypocrites and a Jewish man… also it was narrated in an authentic narration that the revelation of this verse due to a dispute between Az-Zubair and a man from Al-Ansar … in this regard, At-Tbari stated that this verse was revealed for the dispute between the Hypocrite and the Jewish as a main cause of revelation in particular and any dispute similar to the one between Az-Zubair and the Ansari in general, as it is the most correct cause of revelation.
That's why, whosoever accused Prophet Muhammad (PBUH) in his ruling is considered a disbeliever; however, the Ansari matter was a slip and the Prophet (PBUH) pardoned the former because his faith was genuine and didn't do it on purpose. Yet, pardoning the Ansari man was from the Prophet (PBUH) only and none is permitted to pardon anyone in this regard. Besides, whosoever isn't satisfied with the ruling issued by the ruler is a sinner." [Ahkam Al-Quran vol.1 pp.578]. And Allah Knows Best.