Why does water exist at 0 degrees Celsius?

Yes. Ice at 0 degrees C is at a lower energy state than liquid water at 0 degrees C. If you cool liquid water to exactly 0 degrees C, but immediately stop, the water is perfectly fine existing at 0 degrees C as a liquid. But if you take any more energy away from it, the loss of energy is shown not as a temperature change but as a phase change. read more

It also depends on pressure. Ice at 0 degrees C is at a lower energy state than liquid water at 0 degrees C. If you cool liquid water to exactly 0 degrees C, but immediately stop, the water is perfectly fine existing at 0 degrees C as a liquid. read more

0 degrees celsius is the temperature where ice melts into water and water freezes into ice. at exactly 0 degrees, both of these "reactions" are occurring, so water is technically both solid water (ice) and liquid water. read more