According to Dr Sharib:

"Al-'Aziz is the one Who does not depend upon anything or anyone. He
is beyond comprehension and understanding.......He solves the
difficulties of others."

He says that: "to emulate the name you should protect your heart from
pride, vanity and hypocrisy. In order to draw close to Him.... you should
control your undesirable actions and carnal desires. You should not
depend upon others."

Appropriate recitation will secure high status and honour and save one
from being dependent on others.

see 'The 99 Most Beautiful Names of Allah' by Dr Zahurul Hassan Sharib

Some other references:

According to Al-Ghazali this name requires the quality of :

1. being rare,
2. being intensely needed,
3. being difficult to access.

God is the perfection of those three because

(1) His rareness is such that He is One, Singular, and nothing is more
(2) everything is in need of Him - depending on Him for existence.
(3) He is impossible to reach as only God knows God.

As regards the quality in humans this name refers to the eminence of the
Prophets and the caliphs and their heirs. Al-Ghazali says -

"The eminence of each one of them is in proportion to their elevation in
rank above easy access and participation and is measured by their
concern for guiding creatures".

(Al-Ghazali - The Ninety-nine Beautiful Names of God. Trans. Burrel/Daher: ITS: 1992.)

In secular/political life the mantle of high office has built into it, however
imperfectly, the qualities described above by Al-Ghazali - rareness,
dependence of others, and difficulty of access. The qualities however
are not necessarily, or often, integral to the personality of the individual
assuming the office. The assumption of such a mantle can lead to a high
price for the individual since it has been truly said that 'power corrupts'.
When the mantle is removed (for instance after elections) then we see
that man or woman as they are. Wise indeed is the one who has not
been deceived into thinking the power was their own. The one who
succeeds in avoiding such corruption is the one whose motivation is a
sincere concern to guide and help others.

Amongst the sufis the assumption of the Gudi, the succession as Head
of the Order, empowers the individual with spiritual Baraka which he
leaves to his successor when he passes on. What is carried with that
individual is the good he has earned from his use of that Baraka
(spiritual blessings) . Hazrat Nizamuddin Awliya has described this in
'The Morals of the Heart' as recorded by his disciple Hasan Sizji.

Bismillah ir Rehman ir Rahim
The Mighty, The Incomparable and Unparalleled One,
The Strong, The Eminent,
and also The Precious.
(Al-'Azeez, Al-Aziiz)
Qur'an 59:23
Allah is He, than Whom
There is no other god:-
The Sovereign, the Holy One,
The Source of Peace (and
The Guardian of Faith,
The Preserver of Safety,
The Exalted in Might,
The Irresistible, the Supreme.
Glory to Allah!
(High is He)
Above the partners
They attribute to Him.
Laaa-'illaaha 'illaa Huu;
- 'Al-Malikul
- Qudduusus
- Salaamal
- 'Mu'minul
- Muhay-minul -'Aziizul
- Jabbaarul
- Mutakabbir:
Subhaanallaahi 'ammaa

(Qur'an 59:23 trans. Y. Ali)
To Allah applies the highest Similitude:
for He is The Exalted in Power,
Full of Wisdom.
wa lillahil-Masalul -'A'laa:
wa Huwal -'Aziizul-Hakim.

(Qur'an 16: 60 trans. Y. Ali)