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There are many health problems which can cause severely dry skin like this. You might want to evaluate your health and make sure none of these problems are affecting you. If you are suffering from a larger condition, it's important to treat it before the cracks reappear and become infected...or before other, more dangerous symptoms come up.  Diabetes is one common example of an illness which can cause severely dry skin in the extremities.  Talk to your doctor for help in figuring out if you have outside health factors. Your body will naturally produce oils which help protect your skin and prevent cracks. However, an incorrect bathing routine can strip your skin of these natural oils and put you at risk. Mostly you'll want to avoid harsh soaps and hot water, since both will send your body's oils running. If you soak your feet, don't use soaps in the water. Generally you want to avoid soap on sensitive skin, like your feet. Water and a washcloth should be more than enough to get them clean. When the air gets really cold, it also dries out. The area you live in might also be naturally dry. This dry air, draws moisture out from your skin naturally. Protect your skin from drying out by evening out the moisture in the air or by protecting your skin. Place a humidifier in your home or office and wear socks and gloves when you go outside. You skin should also be protected from the sun, which can create damage and dryness over time. If the cracks you experience are mainly on your feet, you might want to take a look at your shoes. Shoes with open backs and poor padding can lead cracks to form by putting too much pressure on already sensitive skin. Use closed shoes and make sure they're very comfortable. Switch to jogging shoes or at least use insoles to protect your feet from pressure. Dehydration can definitely make your skin more prone to being dry and when you combine it with improper washing and a dry environment, it's a recipe for cracked skin. Drink plenty of water each day to keep your body properly hydrated. How much is the right amount depends on the individual person. Generally, if your pee is pale or clear, you're getting enough. If it's not, you need to drink more water. Your skin needs lots of vitamins and nutrients in order to keep growing in healthy. You can make some improvements to the quality of your skin by making sure that nutrient deficiency is not the source of your problem. Get lots of vitamin A, vitamin E, and omega 3 fatty acids, to help your skin get what it needs to be healthy. Good sources of these nutrients include: kale, carrots, sardines, anchovies, salmon, almonds and olive oil. Obesity and excess weight are commonly attached to conditions of severely dry skin. If you find yourself unable to beat this dry skin problem and no outside health factors are in play, you will want to consider trying to lose weight. Remember that this cracked skin poses a serious risk of infection: while the problem might seem small, it can actually be very dangerous and you shouldn't dismiss the problem. Again, if you are ever concerned because the cracks won't go away or because they're infected, please see your doctor or go to a clinic. This is a common problem and there are many solutions available. You doctor should be able to help you figure out if this is a problem you can beat with a routine, or if medication will be needed to help prevent infections.
Check for health problems. Avoid removing your natural oils. Protect your skin from the elements. Change your shoes. Drink more water. Get proper nutrients. Evaluate your weight. Talk to your doctor.