Explain what happens when you add sodium chloride to boiling water.

I know that when sodium chloride is added to water, the boiling point of water increases. What happens when it is added to already boiling water? I know it increases the temperature, I just don't know why...

I have broken this down into two questions. The first one is about turning water into steam.
The Na+ and Cl- ions become hydrated and that makes the intermolecular forces harder to overcome. More energy must be added to allow the kinetic energy of the molecules to escape the liquid state into the gaseous state.

The second one is about why the boiling point is incrreased. The primary reason is because the vapor pressure of the water is lowered. The boiling point is reached when the vapor pressure of the liquid equals atmospheric pressure. When NaCl is added, the vapor pressure of the solution is lowered and that means the temperature must now be higher than 100 in order to reach 760 mm Hg. I hope this makes sense to you. It would be easier to explain if we could draw a vapor pressure curve on the computer.

So if I am trying to put this in a short answer, could I say that when sodium chloride is added to already boiling water the "vapor pressure of the solution is lowered, which means that the temperature must now be higher than 100C in order to reach 760 mm Hg."

That sounds good to me.

Yes, that is a good summary. When sodium chloride is added to already boiling water, the vapor pressure of the solution is lowered, which means that the temperature must be higher than 100°C in order for the water to reach the boiling point of 760 mm Hg.