Very basically: it's a model of your bump that is made using plaster sheets. They're soaked in water and shaped over your belly, and then once dried it is removed, leaving a perfect replica of your pregnant bump.
However, a bellycast is more than just a replica of your bump. Having a bellycast made is a wonderful way of celebrating your pregnant body. A woman's body goes through immense changes during pregnancy, and the uterus grows to around 500x its usual size (or more if you're carrying multiples)! These changes are profound and beautiful, and one way you can honour them - and remember them forever - is by having a cast made.
You could even have several made to chronicle your body changes as your pregnancy progresses, if you wanted to.