A Hash is a number which represents a document in some way. For instance, adding up the value of all the charactors would be a simple hash. Usually you want the hash to have a reasonably small number of possible values, so you modulo it some number, say 256. You also want a hash to be reasonably distributed in that range. My example hash kinda fails on all these counts :)

Hashes are useful for looking up documents. This is called a HashTable. Someone wanna explain this? I tried and did an abysmal job.

Hashes are also used in security, they are called CryptographicHash's