The picture below depicts how the nipple is moved during a breast lift or a breast reduction. The picture shows the nipple left as an island of areolar skin/nipple surrounded by an area that is “deepithelialized”, or removed from the outer most layer of skin, the epithelium.
The whitish brilliant layer surrounding the island of areola/nipple is named the dermis. Many blood vessels run right below that layer, as do some nerves, which preserve the viability and sensation in most cases (losing viability and losing sensation is a small risk). Notice the nipples yellow fat visible in the portion of the breast that is about to be removed during a small breast reduction. Most lifts will include a tiny removal of breast tissue to make for better reshaping of the breast, but a breast reduction will entail much more removal of tissue as compared to a lift.