Explanation

Al-Aliyy is The One Who is above and exceeds all others, The Most High, above whom there is nothing higher, The One whose rank and station are the Most High and The One who is above and surpasses all that has ever been, all that there is, and all that shall ever be.

It has numerous Arabic connotations such as to be high, elevated, lofty, to be exalted, to rise up, to ascend, to be higher, to exceed, surpass, to overcome, overwhelm, to advance, promote, rise above to mount, be overtop, eminent

Quran References

Men are in charge of women by [right of] what Allah has given one over the other and what they spend [for maintenance] from their wealth. So righteous women are devoutly obedient, guarding in [the husband’s] absence what Allah would have them guard. But those [wives] from whom you fear arrogance – [first] advise them; [then if they persist], forsake them in bed; and [finally], strike them. But if they obey you [once more], seek no means against them. Indeed, Allah is ever Exalted and Grand. (Quran 4:34)

That is because Allah is the Truth, and that what they call upon other than Him is falsehood, and because Allah is the Most High, the Grand.  (Quran 31:30)

To Him belongs whatever is in the heavens and whatever is in the earth, and He is the Most High, the Most Great. (Quran 42:4) 

And it is not for any human being that Allah should speak to him except by revelation or from behind a partition or that He sends a messenger to reveal, by His permission, what He wills. Indeed, He is Most High and Wise. (Quran 42:51)