What does it mean to "bind" my breasts?

Wrapping your breast. Breast-binding used to be recommended as a way to help decrease milk supply or help with engorgement. It involves tightly compressing your breasts. It is not recommended as it can lead to mastitis and blocked ducts and other complications. The way that milk supply is decreased is through a hormone feedback system, not compression, and so binding should be avoided.
Ace-wrapping chest. Binding your breast means taking a long wide cloth and wrapping this around your chest tightly. You could also use a wide ACE wrap. This is done in an effort to soothe the discomfort from engorgement during weaning.