This beautiful name of Allah came in the verse 85 of surah Al-Nisaa (An-Nisaa). The English translation of the verse is:
85. Whosoever intercedes for a good cause will have the reward thereof, and whosoever intercedes for an evil cause will have a share in its burden. And Allah is Ever All-Able to do (and also an All-Witness to) everything.
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Allah provides to every one of HIS creation its strength, its sustenance and whatever it/he/she needs, and watches and controls them according to Allah’s wisdom and knowledge. Allah said in surah Hood verse 6, (its English translation is):
6. And there is no creature on earth but that upon Allah is its provision, and He knows its place of dwelling and place of storage. All is in a clear register.
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Thus Allah sends power to His creature and distributes provision to all of the big and small creatures.
For the creatures, Allah managed the power/strength and provision by providing and managing it in the earth during its creation as Allah said in surah Fussilat 10, its English translation is:
10. (41:10) (After creating the earth) He set up firm mountains on it, blessed it,*11 and provided it with sustenance in proportion to the needs of all who seek (sustenance). All this was done in four days.
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Exp.note *11:
Blessings of the earth imply those measureless and countless things which have been continuously coming out of it since millions and millions of years, and are fulfilling the ever increasing needs and requirements of all the creatures from the microscopic germs to the highly civilized man. Among these the principal blessings are the air and the water by which alone vegetable, animal and then human life became possible on the earth.
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[This exp. note 11 and translation of this verse 10 of surah Fussilat is from Tafheemul-Quraan at tafheem.net (towards understanding Quraan. ) The other name of the surah Fussilat is Ha-Meem Al-Sajdah].
Thus Allah managed all of the necessities of the dwellers of the earth like land for cultivation, water, plants and crops; businesses and their profits and losses etc. in the very beginning.
There are also other meanings of Al-Muqeet as Ibn. Katheer said in the tafseer of the verse 85 of surah Al-Nisaa:
Ibn.Abbaas, Ataa, Atiyyah, Qatada and Matar Al-Waraaq said that Muqeeta means Hafeeza (Guardian). Mujaahid said that it means Haseeba (The One Who takes the account.)
Sa’eed Bin Jubair, Suddi and Ibn. Zaid said that it means Qadeera (The One Who has power over all things).
It is possible that “Al-Muqeet” gives all of the above meanings as Allah Almighty has complete knowledge about HIS servants /creature/ creation and also about their circumstances and knows whatever they need. So it is Allah who strengthens the bodies of the servants by food/provision and strengthens their hearts (whomever HE wants) with knowledge and faith.