GD Mail Queue Pro plugin has support for custom SMTP services for PHPMailer. One of the services included is for the Mandrill email sending service. And, to start using this service to send emails using SMTP you need to have paid MailChimp account to get access to Mandrill. After you have set up your MailChimp and Mandrill accounts, you need to get SMTP API Key to add to the GD Mail Queue Pro plugin Mandrill Service settings panel.
To get the required information, open your Mandrill account, and find the SMTP & API Info page to get the login information for SMTP. SMTP password is essentially any of the active API keys you may have for your account.