Subḥān Allāh (سبحان لله), also known as Tasbīḥ (تسبيح), is a well established phrase amongst the Muslims declared daily by many across the world. When this phrase is in use, it is usually said as an expression of freeing Allāh from all deficiencies & anything that which is unbefitting to Him; such as in al-Qurʾān:
ذَٰلِكَ عِيسَى ٱبۡنُ مَرۡيَمَۖ قَوۡلَ ٱلۡحَقِّ ٱلَّذِي فِيهِ يَمۡتَرُونَ مَا كَانَ لِلَّهِ أَن يَتَّخِذَ مِن وَلَدٖۖ سُبۡحَٰنَهُۥٓۚ
That is ʿĪsā, the son of Maryam – the word of truth about which they are in dispute. It is not [befitting] for Allāh to take a son; Exalted is He!
– Sūrah Maryam, ʾĀyāt 34-35
وَقَالَتِ ٱلۡيَهُودُ عُزَيۡرٌ ٱبۡنُ ٱللَّهِ وَقَالَتِ ٱلنَّصَٰرَى ٱلۡمَسِيحُ ٱبۡنُ ٱللَّهِۖ ذَٰلِكَ قَوۡلُهُم بِأَفۡوَٰهِهِمۡۖ يُضَٰهِـُٔونَ قَوۡلَ ٱلَّذِينَ كَفَرُواْ مِن قَبۡلُۚ قَٰتَلَهُمُ ٱللَّهُۖ أَنَّىٰ يُؤۡفَكُونَ ٱتَّخَذُوٓاْ أَحۡبَارَهُمۡ وَرُهۡبَٰنَهُمۡ أَرۡبَابٗا مِّن دُونِ ٱللَّهِ وَٱلۡمَسِيحَ ٱبۡنَ مَرۡيَمَ وَمَآ أُمِرُوٓاْ إِلَّا لِيَعۡبُدُوٓاْ إِلَٰهٗا وَٰحِدٗاۖ لَّآ إِلَٰهَ إِلَّا هُوَۚ سُبۡحَٰنَهُۥ عَمَّا يُشۡرِكُونَ
The Jews say, “Ezra is the son of Allāh”; and the Christians say, “The Messiah is the son of Allāh.” That is their statement from their mouths; they imitate the saying of those who disbelieved [before them]. May Allāh destroy them; how are they deluded? They have taken their scholars and monks as lords besides Allāh, and [also] the Messiah, the son of Maryam. And they were not commanded except to worship one God; there is no deity except Him. Exalted is He above whatever they associate with Him.
– Sūrah at-Tawbah, ʾĀyāt 30-31
وَجَعَلُواْ بَيۡنَهُۥ وَبَيۡنَ ٱلۡجِنَّةِ نَسَبٗاۚ وَلَقَدۡ عَلِمَتِ ٱلۡجِنَّةُ إِنَّهُمۡ لَمُحۡضَرُونَ سُبۡحَٰنَ ٱللَّهِ عَمَّا يَصِفُونَ
And they have claimed between Him and the jinn a lineage, but the jinn have already known that they [who made such claims] will be brought to [punishment]. Exalted is Allāh above what they describe!
– Sūrah aṣ-Ṣāffāt, ʾĀyāt 158-159
أَمۡ لَهُمۡ إِلَٰهٌ غَيۡرُ ٱللَّهِۚ سُبۡحَٰنَ ٱللَّهِ عَمَّا يُشۡرِكُونَ
Or have they a deity other than Allāh? Exalted is Allāh above whatever they associate with Him.
– Sūrah aṭ-Ṭūr, ʾĀyah 43
Another instance is when some of the Companions after just recently accepting Islām asked The Prophet ﷺ to make them a tree similar to a tree of the polytheists, so The Prophet ﷺ replied:
Subḥān Allāh! This is like what Mūsā’s people said: ‘Make for us a god like their gods.’ [7:38]. By the One in Whose Hand is my soul! You shall follow the way of those who were before you.Jāmiʿ at-Tirmidhī #2180, Musnad al-Ḥumaydī #850, Ṣaḥīḥ ibn Ḥibbān #6667 | Ṣaḥīḥ to Imām ibn Ḥibbān, Shaykh Zubayr ʿAlī Zay, and others — Ḥasan Ṣaḥīḥ to Imām at-Tirmidhī
Simply uttering the phrase Subḥān Allāh also has it’s virtues; from them being the notable act of repeating it after every Ṣalāh, repeating it before bed, & other acts.   Among some of it’s other virtues as stated by The Prophet ﷺ are:
There are two statements that are light for the tongue to remember, heavy on the scales, and are dear to the Merciful (Allāh): Subḥān Allāhi wa Bihamdihi, Subḥān Allāhi Adhīm.Riyāḍ aṣ-Ṣāliḥīn #1408 | Muttafaqun Alayh, Ṣaḥīḥ to both Imām al-Bukhārī and Imām Muslim
Purity is half of ʾĪmān. Alḥamdulillāh fills the scales, and Subḥān Allāh and Alḥamdulillāh fills that which is between the heavens and the earth. Ṣalāh is a light, charity is a proof, patience is illumination, and the Qurʾān is a proof either for you or against you. Every person starts his day as a vendor of his soul, either freeing it or bringing about it’s ruin.Ṣaḥīḥ Muslim #223, al-Arba’īn an-Nawawīyyah #23
Subḥān Allāh is commonly translated in English to mean “Exalted is Allāh” or “Glorified & Exalted is Allāh”, but it’s actually much more than that, as Shaykh Muḥammad ibn Ṣāliḥ al-‘Uthaymīn رحمه الله (d. 1421 AH/2001 CE) explains: “As for Subḥān, it is a verbal noun in the accusative considering it an unrestricted acussative from the word(s) ‘sabbaḥa’ (he glorified), ‘yusabbiḥu’ (he glorifies), (and) ‘tasbīḥan’ (glorification). And when a word occurs in the meaning of it’s infinitive form while not actually structured with it’s letters; such is a verbal noun. For instance; ‘salām’ is the verbal noun form of the word but it’s infinitive form is ‘taslīm.’ So, Subḥān is an unrestricted acussative, and so, it must occur in the accusative case and it’s governing word. Thus, it cannot occur with a verb; (therefore) do not say for example; ‘sabbaḥta Allāha subḥānan’ except very rarely (such as) in poems and the likes. Tasbīh means declaring Allāh free from whatever is unbefitting, any deficiency, fault, or likening Him to His creatures or things like that.” 
All praise is due to Allāh, may His peace & blessings be upon our final Prophet Muḥammad, his family, his companions, & all those who follow him in guidance.
 Ṣaḥīḥ Muslim (صحيح مسلم) by Imām Muslim | Ḥadīth #1419
 Ṣaḥīḥ al-Bukhārī (صحيح البخاري) by Imām al-Bukhārī | Ḥadīth #3113
 al-Qawl al-Mufīd Sharḥ Kitāb at-Tawḥīd (القول المفيد شرح كتاب التوحيد) by Shaykh Muḥammad ibn Ṣāliḥ al-‘Uthaymīn | Volume 2, Pages 525-526
Ṣafīullāh Labīb ibn Salīm ʿAbd al-Malik
7th of Muḥarram 1444