How does atmospheric pressure affect boiling points?
The boiling point is reached when the vapor pressure of a liquid matches the atmospheric pressure. Raising the atmospheric pressure will raise the boiling point. Conversely, lowering the atmospheric pressure will lower the boiling point of the liquid.
This phenomena is due to the fact that the vapor pressure of water is temperature dependent. It is raised as temperature increases, and is lowered as temperature drops.
You can think of atmospheric pressure as pushing the liquid in a container back into the container (preventing it from transitioning to the gas phase). The greater the pressure, the more force is pushing the particles down into the container which means you'll need to heat the liquid even more in order to get it to boil.
Reducing the pressure means there is less force pushing liquid particles to stay in a container, so they are able to leave (transition into the gas phase) more easily.
Here is a video that demonstrates this concept: