A convex function is a type of mathematical function where a line segment connecting any two points on the graph of the function lies above or on the graph itself. This property means that the function curves upwards, and it has a unique minimum point. In simpler terms, if you pick any two points on the curve and draw a straight line between them, the line will never dip below the curve. Convex functions are important in various fields, including economics, optimization, and machine learning. They help in finding optimal solutions efficiently, as many algorithms rely on the properties of convexity to ensure that they converge to the best possible outcome.