In a vacuum, the vapor pressure of a liquid equals exactly the pressure of the gas above its surface. However, in gas mixtures, the partial pressure of the respective gas must be considered instead of the total pressure. The partial pressure describes the pressure exerted by each individual gas component in a mixture and is, as one might expect, proportional to the number of particles of that gas within the mixture. This relationship is known as Dalton's Law.
Let us assume that the air pressure at sea level is exactly 1 bar, which is a good approximation in most cases. Air is composed of approximately 78% nitrogen, so the partial pressure of nitrogen is about 780 mbar. In the same way, one can determine the partial pressures of other gases like oxygen and carbon dioxide.
As long as the partial pressure of water vapor in the air remains below the vapor pressure of water at a given temperature, water continues to evaporate into the atmosphere. The reason this process is relatively slow, and not all the water evaporates immediately, is that the other gases in the air exert pressure on the water surface, effectively "holding back" the water molecules.
However, when the boiling point is reached, the vapor pressure becomes greater than the surrounding atmospheric pressure, and the liquid begins to boil. For water, this occurs at around 100 °C when the atmospheric pressure is approximately 1 bar.
At high altitudes, the air pressure is much lower, meaning that water boils at lower temperatures. A famous anecdote mentions that on Mount Everest, where the air pressure is about 330 mbar, water boils at only around 70 °C. This makes it impossible to cook eggs properly there, since the egg white (ovalbumin) requires a temperature above 80 °C to coagulate.