The Most Strong, Perfect Power, The One with inexhaustible strength.
Allah ٱلْقَوِيُّ is Al-Qawiyy (in Arabic: ٱلْقَوِيُّ), meaning the one who commands all power and whose strength is unparalleled to anything else. His strength is truly unlimited and inexhaustible. Man's strength does not compare to that of Allah the Almighty.
From the root qaf-waw-ya (ق و ي), which has the following classical Arabic connotations: to be strong, vigorous, potent, to be robust, hardy, sturdy, to have sufficient strength or power, to prevail over.
The name Al-Qawiyy (sometimes written as Al-Qawi) is mentioned a total of nine times in the Qur'an. It refers to Allah's attribute of being strong. The one who has perfect power. He is eternal; death is not something that touches Him. From Ayatul Kursi, "Neither drowsiness overtakes Him nor sleep." (Qur'an 2:255) No weakness or deficiencies reach Him. His strength is inexhaustible and overcomes all.
He is the most strong. To be strong is a broader concept than power or some manifestation of physical strength. In a sense it describes Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ entity as being perfected. He does not suffer from any weakness, whether it be His sight, hearing, judgment, or knowledge. He can provide whatever for whomever. With regard to His life, it is absolutely enduring forever. He is strong in all aspects - there are no exceptions.
Because of His perfect strength, we rely upon Him for our success alone. Given a choice between two leaders, you would likely choose the one whose power was unmatched (assuming they are not morally corrupt). Similarily, Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ has unlimited capacity and possess superior judgement. He is the only one who can provide the comfort and protection we seek. For this reason, this name is often mentioned in pairs with Al-Aziz (The Mighty) or Al-Matin (The Firm). Imam Al-Ghazali has noted, "Strength indicates perfect power, while firmness indicates intensification of strength." Allah's decree is immovable. Whatever He wills will happen, and nothing can prevent it.
Qaalat ihdaahumaa yaaa abatis taajirhu inna khaira manistaajartal qawiyyul ameen
"One of the women said, 'O my father, hire him. Indeed, the best one you can hire is the strong and the trustworthy.'" — (Qur'an 28:26)
Maa qadrul laaha haqqa qadrih; innal laaha la Qawiyyun 'Azeez
"They have not appraised Allah with true appraisal. Indeed, Allah is Powerful and Exalted in Might." — (Qur'an 22:74)
Allahu lateefum bi'ibaadihee yarzuqu mai yashaaa'u wa Huwal Qawiyyul 'Azeez (Section 2)
"Allah is Subtle with His servants; He gives provisions to whom He wills. And He is the Powerful, the Exalted in Might." — (Qur'an 42:19)
He has unlimited capability and should be feared in the sense that if He chose to go against you, you would be helpless. In the Qur'an, "If Allah should aid you, no one can overcome you; but if He should forsake you, who is there that can aid you after Him? And upon Allah let the believers rely." (Qur'an 3:160) Nothing is able to stand on its own. There is a consequence when we exercise or use any strength or power. In a physical sense, for example, in lifting weights, we get tired and need to rest. There is a limit to what we're capable of. Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ does not get tired. He created the entirety of the universe with ease and can do so many times over. Our moment-to-moment existence is because Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ sustains it until the appointed time. There is not a thing that has indepence or strength but Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ.
Supplication of Prophet Muhammad ﷺ:
It was narrated that Abu Musa said: "The Prophet ﷺ heard me saying: 'La hawla wa la quwwata illa billah (there is no power and no strength except with Allah).' He said: 'O 'Abdullah bin Qais! Shall I not tell you of a word which is one of the treasures of Paradise?' I said: 'Yes, O Messenger of Allah.' He said: 'Say: La hawla wa la quwwata illa billah (There is no power and no strength except with Allah).'" 
From this comes humility in understanding whatever strength or ability we possess, it is from Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. We should derive power and confidence from our belief in Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. This is like when Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ commanded Musa (as) with His message to "Go to Firaawn; (Pharaoh) Indeed, he has transgressed." (Qur'an 20:24) Can you imagine criticizing any King, let alone the tyrannical King of Egypt, and say to him that he has transgressed? It is quite paradoxical; our fear in Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ should be a source of courage and strength in this life to do what is right. To stand up in the face of injustice and to try and aid those oppressed. The strong believer is the one who believes in the most strong, Al-Qawiyy.
Laqad arsalnaa Rusulanaa bilbaiyinaati wa anzalnaa ma'ahumul Kitaaba wal Meezaana liyaqooman naasu bilqist, wa anzalnal hadeeda feehi baasun shadeedunw wa manaafi'u linnaasi wa liya'lamal laahu many yansuruhoo wa Rusulahoo bilghaib; innal laaha Qawiyyun Azeez
"We sent aforetime our messengers with Clear Signs and sent down with them the Book and the Balance (of Right and Wrong), that men may stand forth in justice; and We sent down Iron, in which is (material for) mighty war, as well as many benefits for mankind, that Allah may test who it is that will help, Unseen, Him and His messengers: For Allah is Full of Strength, Exalted in Might (and able to enforce His Will)." — (Qur'an 57:25)
Wa raddal laahul lazeena kafaroo bighaizihim lam yanaaloo khairaa; wa kafal laahul mu'mineenal qitaal; wa kaanal laahu Qawiyyan 'Azeezaa
"And Allah repelled those who disbelieved, in their rage, not having obtained any good. And sufficient was Allah for the believers in battle, and ever is Allah Powerful and Exalted in Might." — (Qur'an 33:25)
Hadith on what makes a believer strong:
It was narrated that Abu Hurairah said: "The Messenger of Allah (ﷺ) said: 'The strong believer is better and more beloved to Allah than the weak believer, although both are good. Strive for that which will benefit you, seek the help of Allah, and do not feel helpless. If anything befalls you, do not say, "if only I had done such and such," rather say "Qaddara Allahu wa ma sha'a fa'ala (Allah has decreed, and whatever he wills, He does)." For (saying) 'If' opens (the door) to the deeds of Satan.'"