The link icon will appear next to a linked row.
A third thing happens when you drag a row onto a shape: A link icon appears for the row in the External Data window. The icon denotes a connection between the data and a shape.
Why is the link icon important? For one thing, when you're working with many rows it's helpful to know which ones are linked and which ones are not. But the link icon is also a helpful reminder when you refresh the data in the diagram. When you refresh the data using the Data menu, all of your data in the External Data window will get updated, and any row that has a link icon will send updates to the shape it's linked to.
Note You don't have to link every row to a shape, so not all rows will necessarily have a link icon. Drag them later. Or don't. You're free to link certain rows or leave some of them unlinked if you want.