Ok well from what I've googled, here are several factors:
Source: Some Univeristy Site
1. Evaporation -- As the initially warmer water cools to the initial temperature of the initially cooler water, it may lose significant amounts of water to evaporation. The reduced mass will make it easier for the water to cool and freeze.
2. Dissolved Gasses -- Hot water can hold less dissolved gas than cold water, and large amounts of gas escape upon boiling. So the initially warmer water may have less dissolved gas than the initially cooler water. It has been speculated that this changes the properties of the water in some way, perhaps making it easier to develop convection currents (and thus making it easier to cool), or decreasing the amount of heat required to freeze a unit mass of water, or changing the boiling point.
3. Convection -- As the water cools it will eventually develop convection currents and a non-uniform temperature distribution. At most temperatures, density decreases with increasing temperature, and so the surface of the water will be warmer than the bottom -- this has been called a "hot top." Now if the water loses heat primarily through the surface, then water with a "hot top" will lose heat faster than we would expect based on its average temperature. When the initially warmer water has cooled to an average temperature the same as the initial temperature of the initially cooler water, it will have a "hot top", and thus its rate of cooling will be faster than the rate of cooling of the initially cooler water at the same average temperature.
4. Surroundings -- The initially warmer water may change the environment around it in some complex fashion, and thus affect the cooling process. For example, if the container is sitting on a layer of frost which conducts heat poorly, the hot water may melt that layer of frost, and thus establish a better cooling system in the long run.
Finally, supercooling may be important to the effect. Supercooling occurs when the water freezes not at 0° C, but at some lower temperature. One experiment found that the initially hot water would supercool less than the initially cold water. This would mean that the initially warmer water might freeze first because it would freeze at a higher temperature than the initially cooler water. If true, this would not fully explain the Mpemba effect, because we would still need to explain why initially warmer water supercools less than initially cooler water.
Confused? Me too.