The meaning of Allah’s name al-‘Aziz
Question

What is the meaning of Allah’s name al-‘Aziz (the Almighty)?
Praise be to Allah.Al-‘Aziz (the Almighty) is one of the beautiful names of Allah. Allah, may He be exalted, says (interpretation of the meaning):
{Verily, your Lord is the Strong, the Almighty [al-‘Aziz]} [Hud 11:66]
{Verily, your Lord is the Almighty [al-‘Aziz], the Most Merciful } [Al-Shu‘ara’ 26:9]
{No indeed [there are no such partners at all]! He is Allah [the only God], the Almighty [al-‘Aziz], the Most Wise} [Saba’ 34:27]
{The sun is rapidly moving towards its destination. That is the decree of the Almighty [al-‘Aziz], All-Knowing} [Ya-Sin 36:38]
{Who has created death and life, so that He may test you [and see] which of you is best in conduct, and He is the Almighty [al-‘Aziz], Oft-Forgiving}[Al-Mulk 67:2].
In linguistic terms, the word al-‘Aziz refers to one who is strong and powerful, who overcomes and cannot be overcome.
Al-Zajjaj said: He is so powerful that nothing can overwhelm Him.
Someone else said: He is the Powerful, the One Who controls all things."(Lisan al-‘Arab, 5/374).
Ibn al-Athir (may Allah have mercy on him) said:
One of the names of Allah, may He be exalted, is al-‘Aziz, Who is the Powerful one Who overcomes and none can overcome Him.
The root word ‘izzah refers to strength, might and control."(Al-Nihayah  3/228).
Al-Zubaydi (may Allah have mercy on him) said:
The word al-‘Aziz comes from the word al-‘izz, which refers to might and dominance. The king is called by this name because he dominates his subjects."(Taj al-‘Arus  15/232).
Al-‘izzah (might), which is one of the attributes of Allah, has three meanings:
‘Izzah in the sense that no one can harm Him.
‘Izzah in the sense of subduing and controlling others.
‘Izzah in the sense of might and power.
All of these attributes belong to Allah, may He be exalted, in the most perfect and complete sense.
Shaykh Muhammad Khalil Harras (may Allah have mercy on him) said in his Sharh:
As for the name al-‘Aziz, it refers to the One who possesses the attribute of might, and the author mentioned three meanings for it:
1. ‘Izzah in the sense that no one can harm Him, so none of His enemies who want to harm Him could do so. Hence their schemes will never reach Him and no one will be able to cause Him harm, as He says in the hadith qudsi: “O My slaves, you can never do Me any harm and you can never bring Me any benefit.” Narrated by Muslim (2577). So no one will ever be able to subdue Him or overcome Him.
2. ‘Izzah in the sense of subduing and controlling others, meaning that He is the Subduer who controls others.
So He, may He be glorified, is the Subduer of His enemies, Who controls and overwhelms them, but they are not able to subdue Him or control Him.
This is the sense in which the word al-‘izzah is most often used.
3. ‘Izzah in the sense of might and power.
These three meanings of ‘izzah may all be ascribed to Allah, may He be glorified and exalted, in the most perfect and complete way that is furthest removed from any shortcomings whatsoever."(Sharh al-Qasidah al-Nuniyyah  2/79).
Shaykh al-Sa‘di (may Allah have mercy on him) said:
Al-‘Aziz means the One Who possesses all might: the might of power and strength, the might of control and overcoming, and the might that prevents anyone from harming Him.
So it is not possible that any of His creation could harm Him, for He subjugates all that exists and all creation submits to His might.
The three meanings of al-‘izzah are all perfect attributes of Allah:
The ‘izzah of strength is indicated by His names al-Qawiy al-Matin (the Lord of Might, the Powerful). This is a description of His great characteristics that cannot be compared to the strength of created beings, no matter how powerful they may be.
The ‘izzah when means that none can harm him indicates that no one could harm Him, for he is al-Ghaniy bi dhatihi (the Self-Sufficient), who does not need anyone and people cannot harm Him or benefit Him; rather He is the one who causes harm and brings benefit, the one who gives and the one who withholds.
The ‘izzah of subjugation and control of all beings. They are all subjugated to Allah, submit to His might and are controlled by His will. All forelocks are in His hand, and none of them can move or do anything except by His power, strength and permission. Whatever Allah wills happens and whatever He does not will does not happen, and there is no power and no strength except with Him."(Tafsir Asma’ Allah al-Husna  p. 214).
And Allah knows best.