Divination comes from the Latin divinare, which means to foresee or to be inspired by God.
To expatiate, divination is the magical art of getting answers or confirmations from a god, by asking it to interact with objects in the physical realm. Divination is condemned in the Bible, but surprisingly it records people using it.
In Judges 6:36-40, Gideon wanted confirmation from God that he would save Israel, so Gideon placed a fleece of wool on the floor, and requested that the dew be on the wool only in the morning and not on the floor. Gideon woke up the next morning to see the fleece with so much dew, that he wrung it out and filled a bowl with water. The floor was dry as Gideon requested.
In 2 King’s 20:8-11, Hezekiah wants to be assured that he will be healed by God, and go up to the house of the LORD on the third day, so the prophet Isaiah gives him a choice of 2 signs. The LORD will move the shadow from the sundial of Ahaz either forward 10 degrees, or backwards 10 degrees. Moving it forwards was unimpressive to the ill Hezekiah, so he asked that it be moved backwards. Isaiah cried to the LORD, and the LORD brought the shadow backwards 10 degrees!
One more instance that I can think of occurs in Acts 1:22-26, where the apostles are looking for a replacement for Judas. They seem to have trouble deciding between Justus and Matthias. So first they pray to the LORD, then the replacement is revealed to them by casting lots.