Promiscuous. The image is that of a woman who is such a pushover that the heels of her shoes became rounded from her being pushed over backwards so frequently. The phrase was popular in men's dormitories and barracks until the sexual revolution changed attitudes.
What does round heels mean?
roundhēld. Sexually promiscuous. Used of a woman. adjective.
What does heel mean in Old English?
"back of the foot," Old English hela, from Proto-Germanic *hanhilon (source also of Old Norse hæll, Old Frisian hel, Dutch hiel), from PIE *kenk- (3) "heel, bend of the knee" (source also of Old English hoh "hock"). Meaning "back of a shoe or boot" is c. 1400.