Pruritus is the medical term for itchiness caused by an irritating sensation on the skin that makes one want to scratch. This can occur anywhere on your skin. The feet are especially vulnerable because people tend to put them in sweaty situations with various types of footwear. Many situations can lead to itchy feet, including exposure to:

moisture
dry environments that lead to dry skin
irritants, when walking barefoot
infectious bacteria, viruses, parasites, or fungi