The polynomial kernel is a function used in machine learning algorithms, particularly support vector machines, to enable learning of non-linear decision boundaries by implicitly mapping input features into a higher-dimensional space. It is defined by the formula K(x, y) = (x ⋅ y + c)^d, where x and y are input vectors, c is a constant, and d is the degree of the polynomial, allowing for flexibility in capturing complex patterns in the data.