The Virus, also known as The Flu, is what causes human beings and possibly other animals to transform into zombies. It appears to work in the same way as the traditional zombie virus, destroying the cortex and other parts that characterize us and allow us to learn, and retains only the stem of the brains, causing the zombie to act only upon its primal instincts. The time for a human to transform into a zombie seems to be very short, ranging from 10-20 minutes.
Interestingly, however, some zombies seem to retain some mentality of their former human selves right before they transformed. For example, when Philip, Shaun's step-father is close to death, he is irritated at Ed's loud music that is being played in the car the group are in, and Ed turns it off. When Philip re-awakens as a zombie in that same car journey only a few minutes later, the rest of the group realize he has transformed and struggle to get out of the car. In said struggle, the music is accidently turned on again, which seems to trigger an even deeper rage in a zombified Philip. Once they are all out of the car and zombie Philip is locked inside, he makes his way over to the cassette player and turns the music off, calming down slightly after doing so. Other examples include a zombified shop owner holding out his hand, seemingly for money, and a zombified homeless person, still holding on to his dog's lead, without the dog, which shows that he may have eaten said dog.