The Customers section is your address book for invoicing. Every invoice must be assigned to a customer, so it's worth keeping this list accurate and up to date.
Open the customer from your Customers list and click Edit. Changes to a customer's details will be reflected on any new invoices created after the change. Existing sent invoices are not retroactively updated.
You can delete a customer from their detail page. Note that you cannot delete a customer who has invoices associated with them. To remove such a customer, you would first need to delete any draft invoices linked to them (sent and paid invoices cannot be deleted).
From a customer's detail page, you can see all invoices ever created for that customer, along with their statuses and totals. This gives you a quick view of the payment history for any individual client.