Conditions such as Athlete's foot, psoriasis, eczema, thyroid disease, diabetes and even some other skin conditions can be the cause of extremely dry and cracked feet.
You can apply some Vaseline to your dry feet which will help seal in moisture and prevent your feet from drying out or apply some regular moisturizer to your feet which can help.
If your feet are constantly dry I would speak with your doctor about it so they can rule out anything else like diabetes that could be causing extremely dry and cracked feet.