In its simplest form, juicing takes the liquid from a fruit or vegetable and squeezes it out, removing the rest of its parts, like pulp, skin or seeds. Juicing allows people to get a more concentrated dose of fruits or vegetables than blending or eating, because the other parts aren't taking any space. For example, a 6-ounce glass of apple juice would use more apples and more nutrients than a 6-ounce apple smoothie. It's much more nutrient rich. Because juicing takes out the pulp and skin, there's no insoluble fiber. This makes juice easier to digest and may be beneficial to people with digestive problems or illnesses, including the elderly.
The key difference between blending and juicing is that blending helps retain every part of the fruit or vegetables, like skin. By keeping every part of the fruit or vegetable, blending allows you to reap the maximum amount nutrients from the food - you know you're getting all of it. Blending also leaves in pulp and other insoluble fibers, which can actually help digestive functions. Additionally, blended drinks release in the system slower, preventing a sugar spike and ensuring a slower release of energy. Blending also allows you to use food that can't be juiced, like bananas or avocados.
Like many aspects of nutrition, there's no easy answer to which is healthier - juicing or blending - it comes down to personal preference and how your body reacts.