When you place the animal cell in distilled water, because distilled water is a hypotonic solution(has a lower concentration than the cytoplasm). Water will diffuse inside the cell through osmosis. This will cause the cell to swell and eventually burst.
When you place the plant cell in the distilled water. The water will diffuse inside the cell, the water will build up inside the vacuole and turgor pressure will appear. The cell won't be able to burst because the cell wall prevents it.
