Some molecules will break free from the solid to enter the liquid phase. Other molecules in the liquid phase will be captured when they bump into the solid and become part of the solid phase. When these two processes are occurring at the same rate, we call this an equilibrium condition. On the macroscopic level we would observe both solid and liquid present, but would not be able to see the changes which were constantly taking place. A substance boils when its vapor pressure is equal to the atmospheric pressure.
Vapor pressure depends only on temperature.
If the actual pressure were 1.1 atm, water could not boil since its vapor pressure would be less than 1.1 atm.