Why will an animal cell burst when placed in freshwater?

Osmosis: The diffusion or movement of water molecules only from a region of high water potential (dilute solution) to a low water potential (concentrated solution) down water potential gradient through a partially permeable membrane.

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.

Note: the cell bursts because the cell membrane is weak and can't tolerate strain or pressure unlike a cell wall (rigid)