A Gaussian kernel is a function used in various machine learning algorithms, particularly in support vector machines and kernel methods. It measures the similarity between two points in a way that emphasizes nearby points more than distant ones. The function is based on the Gaussian distribution, which is a bell-shaped curve, and it helps in transforming data into a higher-dimensional space to make it easier to classify. The formula for the Gaussian kernel involves the distance between two points and a parameter called the bandwidth, which controls the width of the kernel. A smaller bandwidth results in a more localized influence, while a larger bandwidth smooths out the influence over a wider area. This property makes the Gaussian kernel useful for tasks like clustering and regression.