The first thing to understand about the sports bra is you don't have to be running a marathon to need one. Any type of up and down motion where the breasts are going to be moving a lot will do the trick. When your breasts move repeatedly, they tend to stretch out which is a bad thing in the opinion of nearly every woman!
To understand the issue, we have to do a quick anatomy lesson. The breasts are primarily comprised of fat. This essentially creates two weighted masses on your chest. When you move up and down or side to side quickly, these weights move in a delayed manner that causes a lot of stress for the anchor mechanisms.
The anchor mechanisms are were we find the root of the problem. Your breasts are anchored to the core of the body by "Cooper's ligaments". Ligaments have a bad habit of stretching over time if put under stress via weight or weighted movement. In practical terms, this means that as your breasts move about, the ligaments are being put under stress and slowly stretching.
A sports bra works by minimizing the movement of the breast when you are in motion. If you think of a woman jogging in place without a bra, her breasts are going to be bouncing up and down, putting massive stress on the anchor of the breasts. A sports bra works by firmly holding the breast to the chest wall. Each breast is full encapsulated, so there is no room for spillage. The girls are also held up against the chest so that no forward and backwards movement is excessive.
As you might imagine, the average sports bra is not exactly the sexiest of undergarments. That's okay because the purpose is to protect the breasts, not enhance an outfit. All and all, a sports bra can be a real savior for most women. Long term, the bra will keep you from suffering the excessive effects of gravity. Short term, it should eliminate any discomfort you might feel when building up a sweat. This alone makes it a critical part of your wardrobe.