Why does an ice cube melt at room temperature?

Actually, an ice cube will start to melt at 33 degrees F.  What does
this question say about the science education of America today?

Daniel2d,

I think your comment is unfair.  I'm sure the questioner knows that
the melting/freezing point of water is 32 degrees F (0 degees C).  The
question is probably, what is it about the intrinsic nature of the
water molecule, that causes it to change between a solid and a liquid
at a particular temperature?

By the way he said "melt" at room temperature, not "start to melt" at
room temperature.

The strictly technical and pedantic answer to your question: An ice
cube doesn't melt at room temperature, it will stay at 0 degrees
celsius (33 degrees Fahrenheit) untill the ice is completely melted.
Only when the ice is completely melted will the temperature of the
system rise. This is because of all the energy put into the ice is
consumed in converting the ice from solid water to liquid water. The
latent heat of fusion/melting of water is 80 Joules per gram (it takes
80 joules to melt or freeze one gram of water).

An ice cube melts at room temperature because it tries to come into
thermal equilibrium with it's enviroment. Heat flows into the ice,
which increases the total energy of the ice. The molecules in the
solid water start to vibrate faster and they get enough energy to
break free of the electromagnetic attraction that holds the solid
water molecules together.

After these electromagnetic bonds break, the water becomes fluid.

If you heat water to it's boiling point the same process occurs. The
molecules vibrate enough and get so much energy that they can overcome
the force of atmospheric pressure and the water molecules escape into
the atmosphere.