There are two theories that I find attractive regarding the prominence of the human breast. AS many have pointed out, human breast are really strange in mammals. Chimps are flat chested and have no problem nursing their young. And most of the female breast is fat tissue rather than milk glands (which grow during pregnancy and are mostly degraded after lactation stops)
theory 1 Human breast are under sexual selection. Men like big breast. So it gets selected for. There is much justification reported such as breast being a status of health (plenty of fat reserves) and estrogen levels, and thus a proxy for fertility.
However I have not seen any real data to back such an idea, such as A-B cup women being less attractive than C-D cup women. Nor data that women with small breast are less fertile than women with bigger breast.
theory 2 Anti smothering device. Human babies have no snout. So without a prominent breast to create an air space between the body of the mother and the nose of the baby, the baby would suffocate itself when nursing. And a chimp baby does have more of a snout than a human baby.
It is an intriguing idea. However it is also known that human breast does grow during pregnancy, becoming more prominent (particularly apparent for women with small breast). And such gains can be lost once lactation stops. So with that said... is there a reason why the female breast needs to be elevated all the time and not just after pregnancy. I have also not encountered any evidence that women with small breast are smothering their babies when breast feeding.
So at this moment I am leaning towards a hybrid idea...a hypothesis of my own.... that the human breast initially became more prominent for a biological reason.. perhaps a truly flat breast which chimps have really does smother babies without a snout. However once these small breast emerged, they came under the attention of men, and were sexual selected to a far larger size that we see today.