The hadith’s explanation is contained in the full text of the hadith!
عن زراره قال سمعت أبا عبد الله ع یقول إن الله تبارک و تعالى خلو من خلقه و خلقه خلو منه و کل ما وقع علیه اسم شیء ما خلا الله عز و جل فهو مخلوق و الله خالق کل شیء* تبارک الذی لیس کمثله شیء
*Al-Tawḥīd* (al-Ṣadūq), p. 105
Neither God resembles creation, nor creation resembles God!
God and creation are unlike one another in every respect!
A name points to something created. Applying a name to God Most High is a way of avoiding the negation of any relation to Him. Since a name applies to created things, this shows that the Creator has no need of names; using them in reference to God is simply necessitated by the creatures’ need and incapacity in their relation to the Creator.
That Allah has no need of names establishes that He has no need of attributes, since names take their meaning from attributes.
The creatures’ relation to the Creator lies between likening Him to creation and denying His attributes. In this relation, the secret of the declarations of God’s transcendence becomes entirely clear—especially the secret of «سبحان الله و الله اکبر».
Whoever can free themselves from both likening God to creation and denying His attributes has attained the perfection of sincerity in divine unity.
عن الحسین بن سعید قال: سئل أبو جعفر الثانی ع یجوز أن یقال لله إنه شیء فقال نعم یخرجه من الحدین حد التعطیل و حد التشبیه.
*Al-Tawḥīd* (al-Ṣadūq), p. 107
In describing Him, we must acknowledge in our hearts that He transcends our descriptions: no description is worthy of Him, and He is beyond all description!
Creatures have no choice but to draw on their highest faculty of understanding when describing the Lord. In other words, they must use the utmost of their capacity to describe their Creator. In truth, created beings perceive and describe Him with the finest tools and fullest expression their existence affords. The highest form of description—the intellectual—is the limit of an individual’s capacity. Under these circumstances, any description will necessarily be intellectual in nature. Yet our Creator transcends the intellect, for He is the source of the intellect itself. An intellectual description is, in effect, an intellectual act of likening: as though, God forbid, an intellectual image of the peerless Creator had been formed. But if we turn away from such description and fall silent about God Most High, we end up with a total denial of divine description.
Since the One Creator has permitted this kind of description through an acknowledgement of His greatness and transcendence, creatures are permitted to describe Him in this way, provided they also acknowledge the inadequacy of their descriptions.
Thus one meaning of «سبحان الله» may be that Allah is beyond our descriptions; and one meaning of «الله اکبر» is that Allah is greater than can be described. In describing Him, we acknowledge that He is higher and more exalted than our descriptions, and transcends them. Our ability to describe Him is limited by our own capacity; it cannot do justice to His incomparable Essence.
The descriptions offered by those wholly devoted to God are declarations of His transcendence and greatness: whatever they use to describe Allah, they both exalt Him through it and declare Him beyond it!