A Gaussian Function is a function of this form:
(x-b)² f(x) = ae - ———————— 2c²
for constants a, b, c, and Euler's number e, 2.71828....
The function plots a Bell Curve, and among its uses is that it is the Probability Density Function of the Normal Distribution (i.e., Gaussian Distribution), which, as per the Central Limit Theorem, describes the probability distribution of summing a specific number of independent random variables. For example, errors in measurement are commonly assumed to include a purely random element and analyzed using the normal distribution and thus a gaussian function.