The border-radius CSS property is used to round the corners of an element. It can take one value for a uniform radius across all corners or multiple values for individual corners. For example, border-radius: 10px; applies a 10-pixel rounded edge to all corners of the element, while border-radius: 10px 5px 15px 20px; applies different radii for the top-left, top-right, bottom-right, and bottom-left corners respectively.