Hashing Algorithms and Security - Computerphile

If "we store the hash" has ever ended a conversation you wanted to follow, start here. Tom Scott explains what hashing algorithms are for: checking that a file is authentic and has not been tampered with on its way to you. He then asks how secure they really are, and why the algorithms in use keep changing as old ones are found wanting. About eight minutes, and the natural first step before the password video that follows it here.