Hash, Line Hashing, Simple MD5 Hashes - Look down below for the answers to your questions:

Hash functions

A hash function is a mathematical function that converts a larger range of data into a small piece of information, often only an integer.
This can serve as a key to an array. Other names for these hashes are: hash sum, hash codes or hash values

Hash tables are used to speed up lookups in larger tables of data, but sometimes hash functions can map two different set of datas to the same hash value.
You must not confuse hash values with checksums, which are a completely different thing.

Links to things related to hash:

Hash function - Wikipedia, the free encyclopedia
Cryptographic_hash_function - Wikipedia, the free encyclopedia
Hashish - Wikipedia, the free encyclopedia
Hash - Hash functions for PHP


Books

Design of Hashing Algorithms
Fundamentals of Computer Security
Hashing in smalltalk

How to md5sum

Because a lot of people ask how to do this, this is how you do an md5sum in linux (this is a checksum, not a hash)
user@linux:~$ md5sum <filename>