سبحان الله وبحمده
Subḥāna Allāh wa bi-ḥamdih
Glory be to God and praise be to Him: a phrase joining the declaration of His freedom from fault with thanks, said on any occasion.
What it means
The phrase joins two acts: tasbīḥ, declaring God free of all imperfection, and ḥamd, praising and thanking Him for His perfection and His gifts. It can be rendered “Glory be to God, and I praise Him”. Faruqi renders it as praise and thanksgiving that belong to God, and says it may be said on all occasions. The Quran has the combined form, as in “Glorify the praise of your Lord before the rising of the sun and before its setting” (20:130). Muslims say it in the ritual prayer, in the morning and evening remembrance, and at the close of a gathering.
Often misunderstood as
Treating it as a repeated word for “thank you” misses that it joins glorification with praise.
What the sources say
The Prophet Muhammad (peace be upon him) said that there are two phrases that are light on the tongue, heavy in the scale and loved by the Merciful: subḥāna Allāh wa bi-ḥamdihi, subḥāna Allāh al-ʿAẓīm (Sahih al-Bukhari and Sahih Muslim). He also said that whoever says it a hundred times in a day has his sins wiped away even if they are like the foam of the sea (Sahih al-Bukhari and Sahih Muslim).
Term and Arabic as listed in Ismail al Faruqi, Toward Islamic English (International Institute of Islamic Thought, 1995), p. 57, listed as SUBḤĀNA ALLAH WA BI ḤAMDIH.. The definition is restated here.