"Glory be to Allah" is the translation almost every English Qurʼān prints for subḥāna-llāh. It is a serviceable translation — but it leans on an English word ("glory") that does not carry what the Arabic does. The Arabic is not first of all a word of praise. It is first of all a word of distance: a declaration that Allah is far above the picture of Him you were about to form.
That is why it is the phrase the angels say without stopping, the phrase the Qurʼān uses to open the Night Journey, and the phrase the Sunnah puts on your tongue thirty-three times after every prayer. Each of those contexts shares the same function: the mind, if left alone, will keep shrinking God down to a size it can handle. Saying subḥāna-llāh is the small habit of refusing to.
We covered all four short dhikr formulas briefly in the meaning of dhikr. Here is the full version of this one — the root, the grammar, and the picture of God the word is built to correct.