Partially Shipped orders are orders that Zentail believes were not fully shipped. The most common example is a multi-line-item order (i.e. more than one SKU) or a multi-unit order (i.e. multiple units of one SKU).
Orders displaying in the Partially Shipped status on the Orders screen are there because there is no record of all units associated with the order being shipped.
If you have an order that is in the Partially Shipped status but is actually fully shipped, please follow this guide to Manually Ship any remaining units on the order that Zentail believes are currently Unshipped.