Temperature and heat are related, but different.
Heat is the flow of energy. If you run water over your hand that is the same temperature as your skin, it will still feel like it is cooling you down.
Water, along with its many other fascinating properties, has a very high specific heat. Since your said simplistic for younger person; this means water requires much more energy in the form of heat to raise the temperature of water by 1 degree, then most other substances.
Energy (an thus heat) are always trying to go to as low of a state as possible. When your swirl the water around and contact the other portions of the glass, the water is able to absorb a substantial about of energy in the form of the heat from the glass, while not actually raising its "heat content" much at all, due to its large specific heat value. This allows the glass to go to a lower energy state, while waters essentially remains the same in this particular case; making the universe and the laws of thermodynamics happy.
It is this flow of heat that makes it feel colder. The heat flows from the glass to the water, and to maintain thermal equilibrium (same temperature) the heat flows from your hand to the glass. The glasses temperature does not cool down on a macroscopic level, you simply feel the flow of heat and your brain interprets it as it being colder, when in fact it is not.