On the Orders page, when you expand an order, to the right of the Payments and Coupons, you have the Order Comments section. Any notes the customer made would show up here.
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You can use this contact the customer, or to leave internal notes about the order.

Contacting the customer:
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You hit the Add Notes button, this expands the Add Comment section. You would fill out your note, and hit the Email Customer button. That will send an email to the address the customer used to make the order.

Adding Notes:
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The process is the same, except you would hit the Admin Comment button. This just adds a note to the order, the customer would not be able to see the note in any way.