energy - How can melting point equal freezing point?

I don't understand how the freezing point of a substance is the same temperature as the melting point of the same substance.

For example, if liquid water freezes at 0 °C how can ice also melts at 0 °C?

Answer

Because melting point and freezing point describe the same transition of matter, in this case from liquid to solid (freezing) or equivalently, from solid to liquid (melting).

What you may not realize is that while water is freezing or melting, its temperature is not changing! It is stuck on $0\ \mathrm{^\circ C}$ during the entire melting or freezing process. It is easier to see this for boiling points. if you put a thermometer in water and heat it, the temperature will rise until it reaches $100\ \mathrm{^\circ C}$, and then it starts boiling. And while it boils, it will stay at $100\ \mathrm{^\circ C}$! All the way until the water has all boiled away. Now if you could somehow trap the steam (gaseous water) and keep heating it, the steam could have a temperature higher than $100\ \mathrm{^\circ C}$.

So to sum this all up, when matter is transitioning from solid to liquid (melting) or liquid to solid (freezing), its temperature is fixed at the melting/freezing point, which is the same temperature.