By default, after a customer signs up for your email newsletter using your Out of the Sandbox theme's form, their email address (and first and last name, if applicable) are stored in your customer database.
In order to send email marketing to them, however, you will need a third party email marketing provider as well as a way to synchronize your customer database with the email marketing system's lists.
For a list of common email marketing provider integrations, check out this article.
