It explains that when an object is immersed partly or completely in a liquid, it loses in weight similar to the weight of the liquid displaced by it.
Let w1 be weight of an object in air and w2 be the weight, when totally immersed in a liquid.
Loss in weight of the object inside the liquid = w1 - w2
When the body is immersed in the liquid, it seems upthrust. The upthrust is same to the weight of the liquid displaced by the object. As the upthrust performs upwards, the weight of the object under the liquid reduces apparently by an amount same to the weight of the unplaced liquid. Hence,
= weight of the liquid unplaced by the object