What the machine does is take a 1/2" by 1/4" portion of your fingerprint and converts it into a three-digit code. When you put your ticket in and place your finger on the reader, it looks for the code. It's not a full print record, and there's about a one-in-a-thousand chance of it being duplicated. (Per a ticket FAQ on a Disney board written by someone who works there.)

The purpose is to keep people from selling partially or fully-used tickets to others (though it prevents any kind of use). Many tourists have been / are scammed by hawkers advertising "cheap Disney tickets" because you can't tell by looking at the ticket what is on the ticket. People shell out lots of money, show up, and find out the ticket is worthless.