greatness: the towering stature of God or the high standing of a person, together with the great deeds and public honor that make it visible
Hebrew already has an ordinary adjective for "great" (גָּדוֹל) and a verb for growing great or making someone great (גָּדַל). This word is the noun that belongs with them. It does not call something great; it names the greatness itself, as a thing that can be put on show, told about, increased, or handed to someone.
When the greatness is God's, it has no floor. Psalm 145:3 says no one can search it out, and the lines around it answer that by reciting what he has done, because in the Bible God's greatness is not an idea admired from a distance but a record of rescue that can be retold. That is why the same word slides between the quality and the acts: David can say God "has done all this greatness" and mean the promise just made to him.
The other half of the word's life is social. In Esther the greatness on display is a Persian king's half year of pageantry, and then the rank that same king hands to Mordecai, who had been nobody at court. Nothing sacred clings to the word itself: it names stature, whoever holds it. David's prayer in 1 Chronicles 29:11 puts it at the head of a short list that also names strength (גְּבוּרָה) and splendor (הוֹד), where it is the broadest term of the set and the others fill it in.