Breasts (n.) Twin fatty deposits on the chest of the mature human female. The purpose of breasts is to attract males by indicating fertility and availability.
It has been argued that since the women of remote tribes do not cover their breasts, their sexual symbolism is purely cultural. This ignores the truth that for a symbol to be symbolic, it must in fact be visible. The proper scientific method would be to show a remote tribesman the pictures of a naked porn star before and after breast augmentation surgery, and ask which he preferred. The journals of anthropology do not show any such experiments, to my knowledge.
Also, it is quite possible that the women of remote tribes shown in old copies of National Geographic would seize the chance to cover their breasts if they had the convenience of cheap fabric.
Breast development is tied to hormones and good health in a way that cannot be faked. The unfakeability of physical indicators in any species is key to their survival through the critical process of sexual selection. The size and shape of breasts is severely impacted by suckling, and thus in the ancestral society that shaped us, proud firm breasts are an almost unfakeable indicator of maidenhood. Put it another way: a woman with nice breasts is more likely to be fertile and healthy, and much less likely to have kids and a large protective husband.
This matters specifically to humans because of the peculiarities of our reproductive model: we bond for life, and invest decades as a parental pair in our young.
Men find female breasts attractive because they are youth and fertility indicators, in the same way as they find long hair, smooth skin, clear eyes, healthy teeth, and an hourglass figure to be attractive.