They will actually explode or burst
So What happens is the pure water outside has a high water potential while the cytoplasm inside the animal cell is a low water potential, water will diffuse down a water potential gradient through the semi-permeable membrane of the animal cell and cause the cell to swell (inflate like a fully-blown balloon), the result is that the delicate, elastic cell membrane can't tolerate the internal pressure coming from the cytoplasm so it tears causing the cell to burst.