A sigmoid function is a mathematical function that produces an "S"-shaped curve, commonly used in statistics and machine learning. It maps any real-valued number into a range between 0 and 1, making it useful for modeling probabilities. The most common form of the sigmoid function is the logistic function, defined as f(x) = \frac11 + e^{-x} , where e is the base of the natural logarithm. In machine learning, sigmoid functions are often used in binary classification tasks, where the output needs to indicate the likelihood of a particular class. They help in transforming linear outputs from models like neural networks into probabilities, facilitating decision-making processes in algorithms such as logistic regression.