The Gaussian distribution, also known as the normal distribution, is a continuous probability distribution characterized by its bell-shaped curve, where the mean, median, and mode are equal, and it is defined by its mean and standard deviation. It is fundamental in statistics and natural sciences due to the Central Limit Theorem, which states that the distribution of the sum of a large number of independent, identically distributed variables tends towards a Gaussian distribution, regardless of the original distribution of the variables.