A hash function is a mathematical algorithm that takes a variable-length input of data, such as text or binary code, and returns a shorter fixed-length output. The purpose of a hash function is to provide an efficient way to store or compare large amounts of data without having to process the entire dataset. Hash functions also have the property that it is infeasible to generate two different inputs that produce the same output, known as 'collision resistance'. This makes them useful for verifying the integrity of data stored in digital form.