From Business Insider article:
"Breasts come in different shapes and sizes, but there's one thing they all have in common: They are unique to humans. More than 5,000 mammalian species inhabit this planet. Yet Homo sapiens are the only life forms with permanent breasts. Some may call this human anomaly sexy, but it also raises the question: Why are human breasts so big? Were they an evolutionary mistake?
Every other mammal develops temporary breasts during ovulation or nursing. Basically their purpose is to produce milk. So once the milk is gone, the breasts disappear. But this isn't the case for female humans, whose breasts form during puberty, not pregnancy. So at some point in our evolution, something changed. Why? For example, in 1987 biologist Tim Caro explored seven existing theories on this subject.One was that breasts allowed newborns to nurse from the hip, giving their mothers more mobility to multitask. But it doesn't explain why breasts stick around after the nursing stage is over.
Perhaps the most popular idea was first proposed by Charles Darwin and later explored by zoologist Desmond Morris in his 1967 book, "The Naked Ape." In it, Morris suggests that breasts evolved as a sex symbol to replace the swelling rear end of other female primates during ovulation. In it Morris suggests that breasts evolved as a sex symbol to replace the swelling rear end of other female primates during ovulation. Once our ancestors started walking upright, the sexual organs were no longer as obvious to spot. So males had no obvious way of knowing when a female was sexually mature, and breasts may have formed as a result. This theory would at least explain why women's chests swell during puberty, but it still can't explain why they stick around after menopause."