The orders section allows to see any orders that your site has made.

The manage orders link displays a table with your orders and it can also be sorted by clicking the header row. The status of each order is color coded and is displayed on the right

You can change the status of an order by selecting the desired orders then choosing a different status in the drop-down box and then pressing the 'Update' button at the bottom of the page.

When you modify an order you a presented with a screen similar to the image. Across the top is several tabs which give you quick access to related information about the order. This includes transactions, previous order history, and any listings associated with this order.

Transactions are responses from the Payment Gateway. Normally if they place an order the gateway will return a transaction id and whether or not the order was completed. With this information logged you can see if they had any problems and also see if they didn't finish the order once they went to the gateway.