The attribute means the Almighty the Exalted One. When addressing the Prophet Musa (Moses peace be upon him), Allah proclaims His Might in [Al Qur'an, Surah An Naml 27:9]:
Al-`Aziz is the One Who Alone has all honour; He is never humiliated, nor is He ever wronged; neither imagination nor intellect can ever conceive Him. The root word of this Attribute is `izz, which means might, power, strength, victory, elevation, non-submission.
"And to Him belongs greatness in the heavens and in the earth, and He is the Mighty, the Wise" (Quran, 45:37)
Al-ʿAzīz, the One who has created the entire universe, the heavens and the earth and has complete control over all of His creation. In fact He is incomparable and unparalleled. No one can stand in His way nor no one is like Him or wield power as He does. The One to Whom belongs might and honour in its entirety:
وَلِلّٰهِ جُنُوۡدُ السَّمٰوٰتِ وَالۡاَرۡضِؕ وَكَانَ اللّٰهُ عَزِيۡزًا حَكِيۡمًا
(48:7) To Allah belong the legions of the heavens and the earth. Allah is Most Mighty, Most Wise.
The above said verse wields the utmost power of Allah for He has all the legions of heaven and earth and can unleash those against those who disbelieve Him and ridicule His messengers and prophets. And this power of strength has been exhibited many times in the history when powerful people like Ad and Thamud vanished, leaving behind the traces of their mighty empires so that the coming generations may learn a lesson and be grateful to Allah, the Most Mighty.
Thus, Al-ʿAzīz is He Who cannot be overcome or in any way harmed, the One Who has no peer nor a similitude, Who is very much needed, Who is victorious and is never vanquished, the Mighty, the Omnipotent Who can never be reached.Often repeated at the end of the Quranic verses: {And He is Al-‘Aziz (the All-Mighty), the All-Wise}. God’s divine name “Al-‘Aziz” occurs in many Quranic verses, such as when Jesus said in the Quran: {If You punish them, they are Your slaves, and if You forgive them, verily, You, only You, are Al-Aziz (the All-Mighty), the All-Wise.} (Al-Ma’idah 5: 118)
Another verse is: {And His (Alone) is the Majesty in the heavens and the earth, and He (Alone) is Al-Aziz (the All-Mighty), the All-Wise.} (Al-Jathiyah 45: 37) And a third verse is: {They (the hypocrites) say: ‘If we return to Madinah, indeed the mightier will expel from it the less mighty.’ But ‘Izah (might, honor and power) belongs to Allah, to His Messenger and to the believers, but the hypocrites know not.} (Al-Munafiqun 63: 8)
You may refer to our post "99 Attributes of Allāh" for complete list of 99 attributes of Allah Almighty with meaning and explanation.
You may also refer to our Reference Pages for knowing more about Islam and Quran
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