Basically it is callusing or thickening of layers of skin to protect an area under pressure. The medical term is Hyperkeratosis. This can usually be dealt with at home.  

What the lay man terms hard skin can basically be defined as:

Flaky skin – due to dryness and or irritation

Hard Skin - thickening of the skin on the ball or soft part of the underfoot

Callus –thickening of the skin over a bony prominence which is often discoloured (red, yellow to dark brown). The skin is dead. A callus usually sticks out rather like a corn does – but do not muddle them up, a callus has no root. They are often found on the top or between toes, on the large toe joint (I don’t mean a bunion – that’s bony) or on the heel.

Cracked Heel (xeorosis) – thickening of the skin over the heel area which leads to cracking.

However, if the calluses or areas of hard skin are causing pain or feel lumpy or the heel is actually open, then you should see a chiropodist or your doctor especially if you suffer from heart or vascular problems or diabetes.

Symptoms

There are other symptoms of hard skin apart from the obvious, inspecting your feet and seeing hard dry skin.

You may experience pain which goes away when you sit or lie down.

You also may notice pain when walking especially bare foot or when wearing thinly soled shoes.

Definitions above are very general and obviously there can be many other causes, any concerns you have with your feet should be made to a medical doctor.