A hash function is a mathematical algorithm that transforms input data of any size into a fixed-size string of characters, which is typically a sequence of numbers and letters. This output, known as a hash value or digest, is unique to the specific input, making it useful for various applications, including data verification and password storage. Hash functions are designed to be fast and efficient, ensuring that even a small change in the input will produce a significantly different hash value. They play a crucial role in ensuring data integrity and are widely used in cryptographic systems to secure sensitive information.