The breast is made up of soft tissue, with a fine line of milk ducts running over the tisue, and under the skin. They are producing milk constantly, and the act of pressing down gently on the breast, will make the milk flow faster while you press down. When you release, the flow drops back to normal.
Breast compression, as Dr Jack Newman explains clearly here, can help when you have a struggling baby who is upset milk isn't coming out fast enough. It's a way of using the milk production system in the breast, to encourage faster flow just when you need it.
Not every mother will need to use breast compressions, but it is a useful tool in the toolbox. It is important to squeeze down gently, in a massage motion, as opposed to a pinch. Restricting the milk ducts, with too tight a bra, or restrictive closing, or pinching them hard, can cause plugged ducts, which are painful, and can lead to mastitis, an infection.