The relationship between energy and air pressure?
Boiling occurs when the vapor pressure of a liquid reaches ambient pressure.  In the example you asked about, water can be made to boil by removing the air in the chamber in which the vessel holding the water is kept.  When the air pressure gets low enough, there is not enough pressure to keep bubbles of water created by the water's vapor pressure from expanding.  We call this boiling.  At atmospheric pressure the water still exerts vapor pressure but the air keeps the bubbles from expanding.  The only way for water to reach the vapor phase here is for it to evaporate from the surface so we see no bubbles.