The primary function of a hashing algorithm is to take an input (or 'message') and return a fixed-size string of bytes. The output, known as the hash, is typically a digest that represents the original data in a unique way. If the input changes by even a small amount, the hash will change significantly, known as the avalanche effect. The key aspect of a hash function is that it is a one-way function – data can be turned into a hash, but the hash cannot be turned back into the original data, ensuring data integrity. Hashes are broadly used to verify data integrity because they can reveal if data has been altered. This is crucial in many applications, such as verifying the integrity of downloaded files or the storage of passwords.