A Hash Function refers to any function used to map data of tentative or arbitrary size to that of a fixed size. Through the Hash Function, an address would be generated in the table should a key be provided. The most basic example of a Hash Function is a Book Call Number. Each book found in a library bears a unique call number and this call number may be treated as an address as it tells users where the book is located in the library.
In cryptography, a Hash Function pertains to a mathematical algorithm that is a one-way function, which cannot be inverted. Usually, finding a message that creates a given hash entails the attempt of brute-force search of potential inputs if these would be able to produce a match. Another option is the use of a rainbow table of hashes that have corresponding matches. Hash Functions or more specifically, Cryptographic Hash Functions are a basic tool of modern-day cryptography. (Also, see Cryptographic Hash Function)