The martlet is an heraldic curiosity, insomuch as that, while it does not exist in Real Life, it is firmly ensconced in the heraldic firmament, and can justify itself.
Principally encountered in coats derived from the attributed arms of Edward the Confessor, where a cross Or is surrounded by four martlets, also Or, the marlet is a footless dove. The ruffles of feathers at the "thigh" remain but of leg there is none. Otherwise the bird is entirely normal (unless you credit allegations that some heralds also chose to depict it beak-less).
The marlet is believed to be inspired by the swallow, which is rarely if ever seen to land. From this the medieval mind conceived of a bird incapable of landing, constantly in flight, even sleeping on the wing (which may, in itself, have been inspired by seeing sea-gulls and the like hanging on the wind apparently asleep). So, never landing, the martlet lost its need for feet and did without them.