A hinged mattress is just as the name implies, a mattress with inner hinges as part of its form. The purpose of the hinges is to allow folding or bending.
A standard mattress, which has a border rod or stiffener along the edge, cannot be bent or folded without damage to the outer edge. Once that rod or reinforcement is bent, the mattress will no longer lay flat. A mattress that is hinged avoids that damage.
A hinged mattress can be found in use in different situations. A king size mattress, due to its size, is extremely difficult to handle. A quality king size mattress will be hinged, allowing ease in moving it through doorways or stairways. Folding beds, such as cots, and sleeper sofas have hinged mattresses. When not in use as a bed they can be folded up within the framework.
People who are bedridden or convalescing often have an adjustable bed with a mattress that has hinges every few inches. The bed and mattress can be elevated at the head or foot, it can fold so the knees are lifted up or a combination of any of these functions.
While the hinged mattress that commonly comes to mind is the one that is folded and stored, there is another that is also referred to as a hinged mattress. This mattress is not hinged, instead it is a standard mattress that is positioned on what resembles a lid of a bed-sized box. The lid is hinged to the box (base). The box is used for storage and can be accessed by lifting the mattress/lid combination. These hinged mattresses are often found where space is limited.