The orders page is where you can see details about who has ordered what from you and what the status of that order is.
The order search interface lets you search just by text or you can refine your results by the status. The plus sign in the search box lets you pick specific attributes to search on. The plus sign on the right of the list lets you add additional attributes to view.
The "Export All" link will output an Excel spreadsheet that you can do more involved calculations on.