Deuteronomy 6:4
Hear, Israel: Yahweh, our God, is one Yahweh.
James 2:19
You believe that God is one, you do right; also the demons believe and tremble.
What does it mean when the Bible says that God is one?
An excellent question.
When Deuteronomy was written, the Jews were henotheists, recognizing that other gods existed (eg Exodus 15:11, 20:3, Deuteronomy 5:7, Numbers 33:4, Judges 11;23-24, Psalms 82:1, 86:8, 95:3, 135:5 ─ Judges is particularly clear).
So I'm guessing when I say it's an assertion that means something like, Our God is No. 1.
By the time we get to the NT, Yahweh has become, in Jewish terms, the only god. Thus in the NT in Mark 12 we find ─
29 Jesus answered, “The first is, ‘Hear, O Israel: The Lord our God, the Lord is one;30 and you shall love the Lord your God with all your heart, and with all your soul, and with all your mind, and with all your strength.’ [...]
32 And the scribe said to him, “You are right, Teacher; you have truly said that he is one, and there is no other but he;
where it clearly means Yahweh is the only God.
(It's also an example of Jesus saying explicitly that he's not God. There's no support for Trinitarianism anywhere in the bible, the NT included.)