What are costs associated with inventory? Why is controlling turnover in the inventory important? How can improvements in inventory management impact profitability?

Well, inventory is a combination of raw material,labor and over head; all the three transfer to Work In Process, and WIP transfer to Finish Goods Inventory.
The is anything from any of the process as describing above.
There is conflicting goal within an organization, the cost can be very complicated to determine, it's the work of purchasing department,finance department,product department.
Inventory turnover shows how fast/slow the inventory move on compared with previous years.
Improvements can be done based in all three departments I have listed, working close together try to avoid any "bottleneck", and increase best usage if time.