Understand why water boils when its vapor pressure is equal to atomspheric pressure

Boiling point (when water boils) happens when vapor pressure is equal to atmospheric pressure. As long as vapor pressure is lower the atmospheric pressure, water WILL NOT BOIL. <-- What does that even mean?

For water to boil, the molecules must have enough kinetic energy to continuously escape from the surface of the water 

But how does that happen?

Boiling/evaporation happens when liquid molecules have enough kinetic energy to escape from liquid to the air. Since heat supplies energy, liquid molecules will eventually obtain enough energy to escape the liquid. Additionally, its vapor pressure exerted by liquid will be high because there are more and more gas molecules in the air colliding with each other.

What is blocking the liquid molecules from escaping?

The atmospheric pressure is preventing it. As mentioned previously, when liquid molecules try to escape, they will exert vapor pressure pushing against the atmospheric pressure. If the vapor pressure is not strong enough, then the atmospheric pressure will push the gas molecules back to liquid molecules; hence no bubbling. If its vapor pressure is equal or higher than atmospheric pressure, then now liquid molecules are free to escape from liquid to gas.