A juice cleanse is a certain period of time when all you typically consume is liquids, specifically water, herbal teas, and fresh fruit and vegetable juices.
Just as important is what you are not consuming when juice cleansing -- any liquids which will tax the body such as coffee, caffeinated teas, milk, soda, pasteurized juice, protein powder mixes, diet drinks and so on. Solid or blended foods are also not consumed as the fiber content activates digestion which is avoided during juice cleansing.
When you juice your fruits and vegetables, you remove the insoluble fiber but keep soluble fiber so you are still getting some fiber in your diet. This juice contains the organic hydration, nutrients, vitamins and enzymes from the plant food. Although you do need insoluble fiber in your diet, going for a certain period of time without it will give your body a chance to spend less energy on digestion.
Around 70% of your energy every day is spent on digestion alone, so when you are eating 3 meals a day plus snacks, you are rarely giving your body a chance to direct energy to deeply cleansing the body and drawing up old acidic waste that is likely causing a whole host of symptoms.