A liquid boils when its saturated vapour pressure becomes equal to the external pressure on the liquid. When that happens, it enables bubbles of vapour to form throughout the liquid; those are the bubbles you see when a liquid boils.
If the external pressure is higher than the saturated vapour pressure, these bubbles are prevented from forming, and you just get evaporation at the surface of the liquid.
But at different pressures, water will boil at different temperatures. For example, at the top of Mount Everest the pressure is so low that water will boil at about 70°C. Depressions from the Atlantic can easily lower the atmospheric pressure in the UK enough so that water will boil at 99°C - even lower with very deep depressions.
Whenever we just talk about "the boiling point" of a liquid, we always assume that it is being measured at exactly 1 atmosphere pressure. In practice, of course, that is rarely exactly true.
All liquids, at any temperature, exert a certain vapour pressure. The vapour pressure can be thought of as the degree to which the liquid molecules are escaping into the vapour phase. The vapour pressure increases with temperature, because at higher temperature the molecules are moving faster and more able to overcome the attractive intermolecular forces that tend to bind them together. Boiling occurs when the vapour pressure reaches or exceeds the surrounding pressure from the atmosphere or whatever else is in contact with the liquid.
