We have hair on almost every part of our body except in a few places like the palms of our hands, and the soles of our feet. This is because the skin has two layers- the epidermics, and the dermis.
The epidermis or outer layer contains sweat glands, nails, and hair follicles from which hair grows. Because the hands and feet are the parts of our bodies which most commonly come into contact with our environment, the epidermis is thicker in these areas to protect us.
This thicker epidermis means that hair follicles don't form- and as a result, no hair grows in these regions. Moreover, the palms and soles, contain excessive nerve terminals, for they are the antennae of our body. If hair grew there, this would affect the sensitivity of these regions, and this is another reason why hair does not grow on our palms.