Of course, there were many West African societies before the Europeans came. They were not all the same. But we can say something about what they had in common.
First, we can say that they were influenced by Islam. Islam had entered North Africa and was brought to West Africa by traders coming across the Sahara. Not all West Africans became Muslim, but the faith had a strong influence on the area by the 1500s.
In general, most West Africans lived in small villages in rural areas. Their society was made up of what we might call clans or "lineage groups." These were groups of extended families who claimed some kinship to one another. They were expected to support and care for their members.
In terms of government, West African kingdoms were generally not as hierarchical as those in Asia or Europe. There were clear distinctions between rulers and the ruled, but the gap was not as wide as it was in other parts of the world.