I'll try to explain hashes, because it's good for people to know (they're used for, for example, storing passwords).
Imagine you take a word and encode it by counting 1 for a, 2 for b, and so on to 26 for z. That would mean that every word would have a number. The numbers wouldn't be unique: for example, and and dna would be the same, as would any pair of anagrams, as well as pairs like band and cnd (sorry I'm using acronyms, but I have to think these things up). So if I gave you the code for band, you wouldn't, and couldn't (provably so, if we want to be formal) know if it was band or cnd that was the original word, because 2+1+14+4=21 and 3+14+4=21.
This would be a "hash" function: hash, because it makes nonsense. I could store the hash value of your password, and you would have to find a word to type which matched it: I would compute the hash, and compare it.
It wouldn't be a secure hash function, because it is relatively trivial to create a word for the number 21 just by trying small words from the dictionary until you find something close to 20-ish, and then changing a few letters. Secure hashes are like hashes (many inputs create the same output) but with several additional properties. Firstly, the distance between hashes of similar inputs is random, so if you are looking for a word to match a particular value, and have a word that gives a similar value, it doesn't help. And secondly, as a corollary of the first, it's not feasible to find the word or words matching a given value of the function other than by searching all possible combinations.
So what is done for fingerprint scanners is that the fingerprint image is taken, in various slightly different versions (to allow for not having your finger straight) and reduced to its essential features. Secure hashes of those values are stored with your name. When you put your finger on the scanner, the image is reduced to its essential features, hashed, and the hashes are searched through to find one that matches and therefore gives your name. The only way to find the essential features that match that hash is to try all combinations of essential features, and many of them will give the same hash anyway (note to nerds: these hash functions deliberately collide at non-trivial probabilities).