MD2, SHA, SHA1 and MD5 are well known. We will probably move to SHA-1, which is the US government approved hashing algorithm, over the next year or two. If you have a hash of a large file you will know if that file has been changed even slightly by comparing the old hash with a current one. This is much more convenient in many cases than storing copies of large files. Sometimes you may also want to encrypt a reference to a document.
Encryption is complex, so encrypting a hash is much faster than encrypting the whole document.
Note that the hash cannot be used to get the document back - just to represent to a particular version of that document.