I'll try to explain this without going into too much detail.
There is a natural equilibrium between the vapor given off by the water and the atmospheric pressure. The boiling point is when the those two pressures equal one another.
Example:
Sea level: The vapor pressure of water at 27oC is 26.7mmHg. The pressure of the atmosphere is 760 mmHg. The vapor pressure at the boiling point of water (100oC) is 760 mmHg (the same as the atmosphere), so the water can now escape into the gas phase.
Imagine we were at the center of Jupiter or something, where the atmospheric pressure is immense. Since I don't want to look it up, let's assume it's something like 10,000mmHg. The vapor pressure of water is still 26.7 mmHg at 27oC, (vapor pressure is a characteristic of a substance, and depends only on the temperature in it's most basic definition -- you can see this in the equation for vapor pressure) but now you have to add a ton more energy to get the water to reach boiling point (ie make the vapor pressure equal to the 10,000 mmHg atmosphere of Jupiter), so the boiling point is going to be higher!
Hope that makes sense in a twisted, convoluted way. I'm currently busy with other things and rushed to write this :\