It uses ML to figure out the "intent" of what the user has said (using a document classifier) and named entity recognition (NER) to extract data from the text (date, location etc).
That is actually the easy part. The harder part is the conversation scripting and state handling. Mutters uses the Ink narration engine (originally designed for dialogue heavy games) for this.
It works pretty well. IMHO :)
I played around with Mycroft's Adapt Intent Parser[0] a couple weeks ago. It's written in Python. I was looking for something open source to replace IBM Watson's Conversation API.
With Mycroft working I quickly realized that I'd need some way to deal with state handling and conversation branching. I don't think Mycroft has a counterpart to the Ink narration component - I'm really curious to dig into that!
There are hosted services like API.ai, wit.ai and Microsoft LUIS. Init.ai has NLP built into their bot building platform. Rasa NLU is an open source NLP project that is very interesting.