I have taken this description directly from the Wikipedia description as it uses the description from the Jewish Encyclopedia: BAT ḲOL: Kohler, Kaufmann; Blau, Ludwig
In Judaism bat kol or bat ḳōl (Hebrew: בּת קול, literally "daughter of voice", voice of God) is a "heavenly or divine voice which proclaims God's will or judgment." It signifies the ruach ha-kodesh (רוח הקודש, "the spirit of holiness") or serves as a metonym [a word, name, or expression used as a substitute for something else with which it is closely associated] for God.
In the Hebrew Bible or Old Testament the characteristic attributes of the voice of God are the invisibility of the speaker and a certain remarkable quality in the sound, regardless of its strength or weakness. A sound proceeding from some invisible source was considered a heavenly voice, since the mass revelation on Sinai was given in that way in Deuteronomy 4:12:
"Ye heard the voice of the words, but saw no similitude; only ye heard a voice".
In this account, God reveals himself to man through his organs of hearing, not through those of sight. Even the prophet Ezekiel, who sees many visions, "heard a voice of one that spoke" (Ezek 1:28); similarly, Elijah recognized God by a "still, small voice," and a voice addressed him (I Kings 19:12–13; compare Job 4:16); sometimes God's voice rang from the heights, from Jerusalem, from Zion (Ezek. 1:25; Jer 25:30; Joel 3:16–17; Amos 1:2, etc.); and God's voice was heard in the thunder and in the roar of the sea.
The concept appears in Dan 4:31:
עוד מלתא בפם מלכא קל מן־ שׁמיא נפל לך אמרין נבוכדנצר מלכא מלכותה עדת מנך
[T]here fell a voice from heaven, saying, O king Nebuchadnezzar, to thee it is spoken; The kingdom is departed from thee.
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