Log History provide historical changes from shop that are being managed. Currently the data provided are order history, product history, and campaign history.
Order history provide the order status history changes from specific order ID. The information you can get from this feature such as what status and when the order status change happen.
Product history provide the product changes from specific product ID. There are several information you can get from this feature such as stock changes, price changes, and product status changes.
Campaign history provide the previous and current product campaign from specific product id. There are several information you can get from this feature such as campaign price, stock campaign, when the campaign is started and ended.