When an area of the skin is consistently rubbed or under pressure, the epidermis thickens to protect that part of the body. While skin that isn't usually rubbed develops blisters in that context, these give way to calluses over the long term. An example is that spot on your foot where your shoes rub. At first you probably got a blister, now you have rougher, thicker skin there and no more blisters.
How do they form? The epidermis, the outer layer of the skin, is made up of skin cells migrating from the underlying dermis layer. These cells are going through a dying process, eventually making up the dead skin layer known as the stratus corneum. When an area of skin experiences continuous friction or pressure these layers are pressed together, causing the dead skin cells to accumulate and thicken instead of slough off.
Sometimes calluses are referred to as corns and have nucleated centers. This causes pain and may be due to viral infection (plantar's warts, bunions - the same bag of cats).
Bones can also get callouses - it's part of the bone repair process. Bone is not the stable structure it's portrayed as. It is constantly being remodeled. Because of this, breaks are repaired by the broken ends forming callouses and then extending towards one another.
|by Marionette, Wikimedia|