Here you can specify which newsletters the current customer is subscribed to receive. To add newsletters, click the Add newsletters button and check the boxes next to the appropriate newsletters in the displayed selection dialog. Newsletters can be removed from the list at any time using the checkboxes together with the Remove selected button. You can also remove all listed items at once by clicking the icon and performing the Remove all action.
More resources concerning newsletters can be found in Developer's Guide -> Modules -> Newsletters.
Further information about customers can be found in E-commerce Guide -> Managing your store -> Customers.