Blackphone's private communications services are provided by the Silent Suite and the best place to read about how it works is here: https://www.silentcircle.com/technology. End-to-end encryption will work if the other phone is not a Blackphone, BUT it will have to have the Silent Suite apps and subscription.
Blackphone ships with a one-year subscription to Silent Suite for the primary phone owner. It also comes with a one-year gift subscription to Silent Suite that may be used by anyone with any Android or iOS phone, so you will be able to securely communicate with other people even if they don't have a Blackphone.
You may also use your Silent Circle web account to purchase a global Silent World calling plan (not included with Blackphone) that protects the Silent Circle/Blackphone "leg" of a call to a regular cell phone or land line. Please see the following for details:
UPDATE: We regret to inform you that the licenses for the bundled services associated with your Blackphone 1 lapsed on 31st March 2016 as advised to your reseller. You may either purchase a subscription at the following link: https://accounts.silentcircle.com/join/ or contact your reseller for further assistance with this matter.