Blue Mail for iOS uses the highest privacy & security authentication available for your provider.
Some providers such as Gmail and Outlook, support OAuth, which means Blue Mail for iOS will not have access to your username and password at all! Instead you will approve Blue Mail for iOS as an application, and let it access your mail, as long as you like.
This process involves authorization directly with your provider (who already know your credentials: username and password) and we are given a token that you can control and revoke at any given time.
You can read about it here: http://techcrunch.com/2012/09/17/google-oauth-2-0-for-gmail-and-talk/.