Hashing

A hash is a fingerprint of some data. Put the same thing in and you always get the same fingerprint out. Change one character and the fingerprint is completely different.

The useful property is that it only goes one way. You cannot work backwards from the fingerprint to the original. That is why it is used to check whether a file has been tampered with, and why well-built systems store a fingerprint of your password rather than the password itself. If they are broken into, the attacker gets fingerprints. Turning those back into passwords is a separate and much harder job.