A cryptographic hash function is a mathematical algorithm that transforms input data of any size into a fixed-size string of characters, which appears random. This output, known as a hash, is unique to each unique input, meaning even a small change in the input will produce a significantly different hash. These functions are essential for ensuring data integrity and security in various applications, such as digital signatures and password storage. They help verify that data has not been altered, as any modification will result in a different hash value, alerting users to potential tampering.