Breasts can get heavy, and the sensation of gravity constantly pulling down on the skin of your chest and on your soft tissue can be very uncomfortable. If you get sweaty, moisture can get trapped underneath and cause rashes or fungal infections. Moving about, they can get in the way of your arm movements and if jumping or running the movement can be downright painful. Imagine piercing your ears with heavy weights and then shaking your head. You would want to minimize their movement!
Historically, women have used woven cloth bandeaus, breast bands, belts, straps, stays, corsets, bralets, bodices and all sorts of things to try to minimize movement and support breast tissue. Bras are just the most common contemporary thing.