Calluses and corns are caused by continuous pressure or friction on an area of skin. This excessive pressure causes the skin to die and become hard, it is in fact part of the body's defence mechanism. A soft corn is formed in a similar way, except that when moisture or sweat is trapped where the corn evolves, the hard core softens. This usually is a problem on the toes. Some people get calluses on their hands epecially people who do a lot of hard work with their hands. Often people involved in various martial arts encourage the growth of calluses on their fists for example.
So why are they a problem? Well in case of the martial arts fighter they are not, they are exactly what his knuckles need to protect the bones in his hands. Foot calluses are a different matter, they would be okay if you went everywhere in your bare feet, but of course we don't. We have to wear socks and shoes and often those shoes are a fashion statement generally the cause of many a callus, especially for ladies.
I was going include a nice picture of a foot callus at the top of this post but the only ones I could find were really gross and would put you off your food for a week.
People really under estimate the pain these calluses can cause, from burning pains to localized pain on the soles of your feet that change the way you walk. Often people with flat feet or fallen arches suffer from hard skin and calluses more than most.