Water boils when the thermal energy in the water, which is a type of kinetic energy which causes the water molecules to move around, exceeds the strength of the hydrogen bonds between the molecules, causing them to separate from the other molecules. This breaking of bonds between water molecules consumes any additional thermal energy added, so that water at boiling temperature does not increase in temperature until the phase change is complete. In normal conditions, much of the water vapor almost immediately turns to steam, which is actually composed of droplets of liquid water because it has left the source of heat.
Heat is not the only factor that affects boiling. Water is held in liquid state not just by the hydrogen bonds between molecules, but also by atmospheric pressure. If the pressure on the water decreases, evaporation increases because this diminishes the forces holding the molecules in place. If pressure is low enough, water will even boil at room temperature.
Boiling is the most extreme form of evaporation, but evaporation of water is constant, as individual molecules happen to break away from the liquid through random movements. Indeed, water molecules randomly escape into a gaseous state even from ice, and this process is known as sublimation.