It looks like you are using the Product Templates feature. The template name (eg. Notes) is stored in the ac_ProductTemplates table. The input values are stored in the ac_ProductTemplateFields table.
That's not quite what I'm interested in. That field is where a customer can leave a note about the product when they order it. I want to see all of the notes left in that box for a particular item.
Is the value users enter into that field stored in the database somewhere?
Sorry. I forgot that the product templates work for both merchant input and customer input. If a customer inputs some text, then you'll need to look at the ac_OrderItemInputs table, column = InputValue. You'll have to join the query to find the product Id though.
You can always find those values from order summary page in Administration. Anything entered will be listed along with purchased item. In database as Katie mentioned the name of table you can find them in ac_OrderItemInputs table.