Non-convex refers to a shape or set that does not have the property of convexity. In a convex shape, any line segment connecting two points within the shape lies entirely inside it. In contrast, a non-convex shape can have indentations or "dents," meaning that some line segments connecting points may lie outside the shape. In mathematics and optimization, non-convex functions can have multiple local minima and maxima, making them more complex to analyze than convex functions. This complexity is significant in fields like machine learning and operations research, where finding the best solution can be challenging due to the presence of these multiple peaks and valleys.