A weighted vest makes your life much easier. Although it is possible to perform exercises such as pull-ups and pushups with a heavy backpack, by holding a dumbbell with your feet (for pull-ups) or a plate on your back (for pushups), that is far from convenient. It is uncomfortable, unsafe, and sometimes hard to pull off.
A weighted vest is a much more comfortable solution as it allows you to perform all movements freely, without standing in your way. Weighted vests have many "pockets" which hold small plates, allowing you to fine-tune the exact amount of weight you need. This gives you much more control than with plates, let alone heavy books in your backpack.
Also, a vest distributes the weight much more evenly, which is better for overall muscle development. And with a vest, the risk of dropping the weight and injuring yourself, or damaging the floor or furniture does not exist - plates are safely inside the vest, strapped to your body.
Some of the exercises that are especially good with a weighed vest include:
But essentially, you can do any type of movement with a vest, making it more difficult. Just be careful - adding more weight puts added stress on your joints, so try not to run a marathon with your weight vest on. It is a better idea to keep your workouts short, but intensive.