'Conversational UX is the way a user experiences an interaction with a business or a service through an automated conversational interface that learns along the way.' 

Somewhat of a mouthful to say! However, this is one of those new 'disruptive' terms which you will hear more and more as ML and AI replace humans in the first digital point of contact in customer support. 

To explain it in simpler terms, it is the conversation that you (user) has with a chatbot, which in turn learns from the different messages you share in the conversation with it. It then adapts its response accordingly, as it learns from you. 

The key part of this term is 'UX'. What is the best way to introduce these new technologies, and enhance the user experience? From the everis Digital Research Lab, one of the reports produced, 'The Cheers and Fears of AI,' identified how to approach your chatbot strategy to gain the trust of the user and to make them feel comfortable interacting with it. 

The study showed some insights around the user experience interaction with chatbots relating to trust and perceptions and external influences like media. And how we interact differently in our working and home lives. And like many other channels, the approach to the user experience needs careful thought. Bring a wide spectrum of users to the centre and involve them at each stage from planning to creation to launch.