To put it very simply: It tried millions of different combinations for the enigma much much faster than the original human group could, therefore eventually cracking it before it was changed again at Nazi High Command. As soon as it was broken the code was sent to the War Office in London to be used. It changed daily so the machine was constantly at work. :)
In the movie it was mentioned that each day started with a weather prediction that contained a phrase that was used each day. This made it easier for Turing's team to map the particular encryption scheme for that day to a known phrase, making their work a lot easier.