I would say any answer must be guesswork, so I will make this a community wiki.

Hash, or hash browns, is breakfast food made from cutting potatoes into long thin strips (smaller than french fries, and shorter, but proportionally similar), then frying the mass of strips in animal or vegetable fat until browned, stuck together, and cooked. By analogy, hashing a number meant turning it into another, usually smaller, number using a method which still deterministically depending on the input number.

I believe the term "hash" was first used in the context of "hash table", which was commonly used in the 1960 s on mainframe-type machines. In these cases, usually an integer value with a large range is converted to a "hash table index" which is a small integer. It is important for an efficient hash table that the "hash function" be evenly distributed, or "flat."

I don t have a citation, that is how I have understood the analogy since I heard it in the 80 s. Someone must have been there when the term was first applied, though.

A hash value (or simply hash), also called a message digest, is a number generated from a string of text. The hash is substantially smaller than the text itself, and is generated by a formula in such a way that it is extremely unlikely that some other text will produce the same hash value.

You re refering to the "hash function". It is used to generate a unique value for a given set of parameters.

One great use of a hash is password security. Instead of saving a password in a database, you save a hash of the password.

A hash is supposed to be a unique combination of values from 00 to FF (hexadecimal) that represents a certain piece of data, be it a file or a string of bytes. It is used primarily for password storage and verification, and to test if a file is the same as another file (i.e. you hash two files, if they match, they re the same file).

Generally, any of the SHA algorithms are preferred over MD5, due to hash collisions that can occur when using it. See this Wikipedia article.

According to the Wikipedia article on hash functions, Donald Knuth in the Art of Computer Programming was able to trace the concept of hash functions back to an internal IBM memo by Hans Peter Luhn in 1953.

And just for fun, here s a scrap of overheard conversation quoted in Two Women in the Klondike: the Story of a Journey to the Gold Fields of Alaska (1899):

They ll have to keep the hash table going all day long to feed us. T will be a short order affair.

the hash function hashes input to a value, requires a salt value and no proof salt is needed to store. Indications are everybody says we must store the salt same time match and new still work. Mathematically related concept is bijection

adding to gabriel1836 s answer, one of the important properties of hash function is that it is a one way function, which means you cannot generate the original string from its hash value.