Answer:
The rose in the poem is people who have grown from nothing into something (an example would be people from a poor neighborhood who are exposed to crime and such and are expected to fall in the cracks of that, who then get themselves out of that environment either physically, mentally, or both and become more than they ever thought they could be.) Damaged petals are the damages the "rose" has received out of coming out of the cement (the damage that the "rose" receives is either emotionally, physically, or both.)