The Laplace Distribution is a probability distribution that is characterized by its sharp peak at the mean and heavier tails compared to the Normal Distribution. It is often used in statistics and machine learning to model data with outliers, as it can better capture the behavior of such data. Mathematically, the Laplace Distribution is defined by two parameters: the mean and the scale parameter, which controls the spread of the distribution. Its probability density function has a distinctive double-exponential shape, making it useful in various applications, including finance and signal processing.