What causes the sensation of burning feet ?

Usually nerve: "burning" is most commonly caused by a nerve, either mechanical, like a nerve compression in the foot, leg or lower back, or from a metabolic disease like diabetes or anemia. If both feet burn, it's more likely metabolic, but if one foot burns, it's probably something local. But if you smell smoke... Run! seriously, go see a podiatrist if it's only one foot, or a neurologist if it's both.

Neuropathy: can be from systemic disease like diabetes, vitamin deficiencies or if unilateral from nerve entrapments. (these are some causes)