The Customer Info field allows you to add Commerce related customer information to the Craft user profile's field layout. This allows you to see the past orders for a customer as well as all addresses they have in their address book.
If you named your customer info field customerInfo you would be able to have a {entry:343:link} returned for a user like so:
{% set customer = user.customerInfo %}Example of getting the customers addresses:
{% for address in user.customerInfo.addresses %}
{{ address.firstName}} <br>
{% endfor %}Example of getting the customers past orders:
{% for order in user.customerInfo.orders %}
{{ order.number}} <br>
{% endfor %}