Signal is a messaging app for Androids and iOS devices. It is widely hailed as the most secure such app available. It uses the ZRTP protocol (Zimmerman Real-Time Transfer Protocol) that reports indicate even the NSA can't crack. Edward Snowden uses the app regularly, and so do members of Congress.
Signal can be used for secure messages, phone calls, and video calls. After installing the app, you enter your phone number, and then submit a verification code.
You can adjust the Privacy Settings so that your IP address is never revealed to the people you are contacting, and prevent signal calls from being listed in your phone call history.
The app also allows user to guard against man in the middle attacks by comparing QR codes. The keys used to encrypt messages are stored on each Signal user's phone.