to practice divination: to seek out or hand on hidden and future knowledge through mantic technique, rather than through a genuine word from God
At its core this is a professional's word. A diviner was a paid specialist who tried to uncover hidden or future things by set techniques: casting or dividing lots, shaking marked arrows, consulting small household images or the dead, or reading the liver of a sacrificed animal. Such specialists worked all across the ancient world, and the Bible can name them plainly and without heat, as it does the Philistine diviners who advise their leaders, or the Babylonian king who halts at a crossroads and shakes his arrows to decide which way to march.
Inside Israel the same activity is placed off-limits. Because Israel already had God's own authorized ways of hearing from him, this whole enterprise became something the nations do and Israel must not (Deuteronomy 18). Even Balaam, a real foreign diviner whom God nonetheless used, is finally labeled simply "the diviner" and put to death. So the word carries a double life: a neutral, descriptive act among the nations, and a forbidden one for the covenant people.
The sharpest turn comes when the prophets aim the word at Israel's own prophets. To brand a message as mere divination was to say it came from the speaker, not from God: when a man only seemed to prophesy (נָבָא), Jeremiah, Ezekiel, and Micah called it divining instead. Micah even jabs that these prophets "divine for money," which is exactly what a diviner had always been, a paid oracle. This is why the same word can describe both a pagan expert and a discredited Israelite prophet.
Behind the whole range lies an old idea of dividing or apportioning by lot. To draw a lot was to be handed your share, so the one root could cover the drawing of arrows, the fee paid for an oracle, and, in the end, any claim to secret knowledge won on human terms.