A breastwork is a fortification. The term is usually applied to temporary fortifications, often an earthwork thrown up to breast height to provide protection to defenders firing over it from a standing position. A more permanent structure, normally in stone, would be described as a parapet or the battlement of a castle wall.
In warships, a breastwork refers to the armored superstructure in the middle of the ship that did not extend all the way out to the sides of the ship. Generally only used in ironcladturret ships designed between 1865 and 1880.