The Necessity of Obeying the Messenger ﷺ
Allah said,
وَمَآ أَرْسَلْنَا مِن رَّسُولٍ إلاَّ لِيُطَاعَ
(We sent no Messenger, but to be obeyed) meaning, obeying the Prophet was ordained for those to whom Allah sends the Prophet. Allah's statement,
بِإِذُنِ اللَّهِ
(by Allah's leave) means, "None shall obey, except by My leave," according to Mujahid. This Ayah indicates that the Prophets are only obeyed by whomever Allah directs to obedience. In another Ayah, Allah said,
وَلَقَدْ صَدَقَكُمُ اللَّهُ وَعْدَهُ إِذْ تَحُسُّونَهُمْ بِإِذْنِهِ
(And Allah did indeed fulfill His promise to you when you were killing them (your enemy) with His permission) meaning, by His command, decree, will and because He granted you superiority over them. Allah's statement,
وَلَوْ أَنَّهُمْ إِذ ظَّلَمُواْ أَنفُسَهُمْ
(If they (hypocrites), when they had been unjust to themselves,) directs the sinners and evildoers, when they commit errors and mistakes, to come to the Messenger ﷺ, so that they ask Allah for forgiveness in his presence and ask him to supplicate to Allah to forgive them. If they do this, Allah will forgive them and award them His mercy and pardon. This is why Allah said,
لَوَجَدُواْ اللَّهَ تَوَّاباً رَّحِيماً
(they would have found Allah All-Forgiving (One Who forgives and accepts repentance), Most Merciful).
One Does not Become a Believer Unless He Refers to the Messenger ﷺ for Judgment and Submits to his Decisions
Allah said,
فَلاَ وَرَبِّكَ لاَ يُؤْمِنُونَ حَتَّى يُحَكِّمُوكَ فِيمَا شَجَرَ بَيْنَهُمْ
(But no, by your Lord, they can have no faith, until they make you judge in all disputes between them,) Allah swears by His Glorious, Most Honorable Self, that no one shall attain faith until he refers to the Messenger ﷺ for judgment in all matters. Thereafter, whatever the Messenger ﷺ commands, is the plain truth that must be submitted to inwardly and outwardly. Allah said,
ثُمَّ لاَ يَجِدُواْ فِى أَنفُسِهِمْ حَرَجاً مِّمَّا قَضَيْتَ وَيُسَلِّمُواْ تَسْلِيماً
(and find in themselves no resistance against your decisions, and accept (them) with full submission.) meaning: they adhere to your judgment, and thus do not feel any hesitation over your decision, and they submit to it inwardly and outwardly. They submit to the Prophet's decision with total submission without any rejection, denial or dispute. Al-Bukhari recorded that `Urwah said, "Az-Zubayr quarreled with a man about a stream which both of them used for irrigation. Allah's Messenger ﷺ said to Az-Zubayr,
«اسْقِ يَا زُبَيْرُ ثُمَّ أَرْسِلِ الْمَاءَ إِلى جَارِك»
(O Zubayr! Irrigate (your garden) first, and then let the water flow to your neighbor.) The Ansari became angry and said, `O Allah's Messenger! Is it because he is your cousin' On that, the face of Allah's Messenger changed color (because of anger) and said,
«اسْقِ يَا زُبَيْرُ ثُمَّ احْبِسِ الْمَاءَ حَتَّى يَرْجِعَ إِلَى الْجَدْرِ،ثُمَّ أَرْسِلِ الْمَاءَ إِلى جَارِك»
(Irrigate (your garden), O Zubayr, and then withhold the water until it reaches the walls (surrounding the palms). Then, release the water to your neighbor.) So, Allah's Messenger ﷺ gave Az-Zubayr his full right when the Ansari made him angry. Before that, Allah's Messenger ﷺ had given a generous judgment, beneficial for Az-Zubayr and the Ansari. Az-Zubayr said, `I think the following verse was revealed concerning that case,
فَلاَ وَرَبِّكَ لاَ يُؤْمِنُونَ حَتَّى يُحَكِّمُوكَ فِيمَا شَجَرَ بَيْنَهُمْ
(But no, by your Lord, they can have no faith, until they make you (O Muhammad ) judge in all disputes between them.)"' Another Reason In his Tafsir, Al-Hafiz Abu Ishaq Ibrahim bin `Abdur-Rahman bin Ibrahim bin Duhaym recorded that Damrah narrated that two men took their dispute to the Prophet , and he gave a judgment to the benefit of whoever among them had the right. The person who lost the dispute said, "I do not agree." The other person asked him, "What do you want then" He said, "Let us go to Abu Bakr As-Siddiq." They went to Abu Bakr and the person who won the dispute said, "We went to the Prophet with our dispute and he issued a decision in my favor." Abu Bakr said, "Then the decision is that which the Messenger of Allah ﷺ issued." The person who lost the dispute still rejected the decision and said, "Let us go to `Umar bin Al-Khattab." When they went to `Umar, the person who won the dispute said, "We took our dispute to the Prophet and he decided in my favor, but this man refused to submit to the decision." `Umar bin Al-Khattab asked the second man and he concurred. `Umar went to his house and emerged from it holding aloft his sword. He struck the head of the man who rejected the Prophet's decision with the sword and killed him. Consequently, Allah revealed,
فَلاَ وَرَبِّكَ لاَ يُؤْمِنُونَ
(But no, by your Lord, they can have no faith).
Tafsir Ibn Kathir (abridged, English).