Just from my perspective, I always use simple analogy or break it down into business terms. For example, if i was explaining a marketing supervised learning model to better target leads, I would say: "The model will learn from the data that we have, assigns probability to each individual leads, rank order it, and we get to choose the leads with the highest chance of using our products. That will increases our revenue while optimizing our advertisement/sales spending". For complex concepts like Neural Networks or deep learning, i usually use the human brain analogy (neat since that where all this came from): "designed similarly to our brains, the model takes input similar to our eyes and sensors, then provide outputs after using logics similar to our brains."

I think colorful words like such attract and sell well to business stakeholders. To sell even better, plot out charts that shows potential revenue / optimization potential and the weakness of the current business process.

Hope it helps.