The suggestion is to prevent a puddle of the liquid present in the sample from forming or from it leaking on to the surface on which it is placed. For example, if precipitates of a solid are removed from water and then placed on filter paper to dry, the water will soak into the filter paper and then leak on to the counter on which it is placed. If this precipitate were placed in a watch glass or weighing paper, the water would only evaporate and would not contaminate the sample.
