The divining arrows (Al Azlam) is where pagans used arrows to make decisions which they deemed to be "divine answers" from their pagan gods.
IslamQA gives a good description of divining arrows:
"During the Jaahiliyyah, they had arrows or pieces of wood, on one of which was written “Do it”; on other arrows were written the words “Do not do it” and “Not clear (or try again)”. A person would draw one of them, and if he found the words “Do it” he would go ahead with what he was thinking of doing; if he found the words “Do not do it”, he would turn away from what he wanted to do and think that it was bad; if he found the word “Not clear (or try again),” he would try again. Thus he was seeking his share of the unseen by means of these arrows, so that if it was good he would pursue it and if it was bad he would forget about it" - IslamQA
From hadith we get a glimpse of how they were particularly used.
Used for making a decision.
"..when I approached them (i.e. Muhammad and Abu Bakr), my horse stumbled and I fell down from it, Then I stood up, got hold of my quiver and took out the divining arrows and drew lots as to whether I should harm them (i.e. the Prophet (ﷺ) and Abu Bakr) or not, and the lot which I disliked came out. But I remounted my horse and let it gallop, giving no importance to the divining arrows.." - Bukhari (3906).
Used for fortune-telling and "omens".
"...when Jarir reached Yemen, there was a man who used to foretell and give good omens by casting arrows of divination.." Bukhari (4357).