In Book of Ezra chapter 10 No.3 the Bible uses the Hebrew word אֲדֹנָי to talk about Ezra.
I thought this word was used only when talking about God.
What does this word mean?
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In the comments, you cite this link. I believe you were confused due to English not being your first language by this sentence: "used as a proper name of God only." In context, that sentence does not mean that the word אֲדֹנָי can only refer to God. It means that the word אֲדֹנָי refers to God when it is used as a proper name.
Indeed, as Yishai pointed out in the comments, that word certainly can be used to refer to people (although the verse in Ezra that you cited does seem to be using אֲדֹנָי to refer to God, not Ezra as you suggest. Rashi confirms this).