A: Probably best to take this one bite at a time:
Encrypted: The process of encoding a message or information in such a way that only authorized parties can access it and those who are not authorized cannot.
Chat: A specific form of electronic communication. Originally containing only text, but in recent years has been upgraded to allow inclusion of images, video, and sound.
Client: The application used by the end-user of the computer or mobile device.
So, and encrypted chat client is an application that allows two or more people to share text and possibly images, sound, and video among themselves, and prevents others from access by way of encoding the communication.
Examples include Apple Messages, Wire, and Signal.