The idea of a juice feast, which is a bit different from a normal juice fast, is that you are supposed to be drinking freshly made juices to get your nutrients and calorie intake. You also take supplements to help you along the way.
The purpose of the juice is to take away as much of the fiber as possible. It is like when you drink a green smoothie, it is easier for your body to absorb the nutrients of lettuce because you have broken it down so your body doesn't use all the energy to try to do that for you. One of the theories, and I don't exactly agree, is that your body uses the energy to burn fat and purge toxins instead of trying to digest all that fiber. That is why juice fasting or feasting sites and books talk about enemas in order to keep things flowing.
In my experience my juices always had fiber as my juicer was not the best quality, so I didn't have to do anything like enemas and stayed really regular throughout. A normal juice day for me would be to drink 1 and a half quarts of green juice and 1 quart of a fruit juice, that usually had some spinach or celery added in for good measure. In addition to that I would drink 2 - 2 and a half quarts of water.
Some people do these juice feasts for 100+ days...I managed 40, but nearing day 40 I was in starvation mode due to my dislike for green juices. I wasn't drinking enough and came off of it and started my new diet earlier than I was expecting. I'm glad I came off of it when I did as I was starting to feel poorly. If I liked the green juices I probably would have stayed on the feast for longer, though maybe not 100+ days.
My life changed after the feast. I can't eat as much, I can't stand sweets like I used to, I also can't stand overly salty things...I also cut out dairy as the thought of it makes me ill. I've continued to lose weight and have not gained it back.