What does the definition of boiling actually mean? Boiling point is defined by wikipedia as:

The boiling point of a substance is the temperature at which the vapor pressure of a liquid equals the pressure surrounding the liquid and the liquid changes into a vapor.
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My question
My question is what exactly are we referring to as "pressure surrounding the liquid" with respect to a closed vessel. Does it mean pressure directly above the liquid surface or the pressure over the lid.

My arguments

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*If it means pressure directly above the liquid surface then, shouldn't this pressure include vapor pressure in it. In this case, the vapor presssure can then never become equal to atmospheric pressure.


*If it means pressure over lid, then why does it matter as it is not directly interacting with liquid and wont try to stop boiling.

Please provide an elaborate picture for the same.
 A: Imagine a glass of water inside a box which is completely evacuated.  There is no gas in the box at all, only liquid water and empty vacuum.  Every so often, an H$_2$O molecule near the surface of the water gets a random kick from its neighbors which is sufficient to free it from the liquid phase and propel it outward into the vacuum.  Through this mechanism, the liquid water evaporates and becomes water vapor.
Initially, there is hardly any vapor at all so the reverse reaction (an H$_2$O molecule in the vapor phase condensing back into the liquid phase) is rare.  As more molecules enter the vapor phase, the rate of re-condensation increases until eventually the condensation rate is equal to the evaporation rate.  At this point, the liquid is in equilibrium with the vapor, and the pressure of the gaseous H$_2$O is called the vapor pressure of H$_2$O.  Note that vapor pressure is a function of temperature; if the glass of water is hotter, the rate at which H$_2$O molecules are kicked out into the vapor phase goes up, which means that the corresponding vapor pressure required for equilibrium will also go up.
If the box was not initially evacuated but rather filled with an atmosphere of, say, pure helium gas, then precisely the same process would take place.  Therefore, the vapor pressure refers specifically to the partial pressure of H$_2$O which will be in equilibrium above its liquid phase, and is not concerned with the pressure due to other gases.

Now consider a pot of water on your stove.  For the sake of argument, let's say your kitchen is completely sealed off from the outside environment except a piston which is exposed to the atmosphere; the purpose of this elaborate setup is to make sure that your kitchen stays at precisely one atmosphere, but no gas may enter or leave.  Assume also for the moment that the gases in the kitchen are perfectly mixed.
As you increase the temperature of the water, the rate of evaporation increases - as a result, the vapor pressure increases as well.  The proportion of H$_2$O vapor in your kitchen increases and the piston is slowly pushed outward, such that the system is always in equilibrium.  At 99$^\circ$ C, the gas in your kitchen is almost all water vapor, but still an equilibrium is maintained.
But then you cross the 100$^\circ$ C point, and the vapor pressure exceeds $1$ atm.  Runaway evaporation now occurs, as the partial pressure of water in your kitchen can never match the vapor pressure (which is the pressure required to maintain the evaporation/condensation equilibrium).  This is boiling.
Now, this situation is obviously artificial.  In real life, your kitchen is not sealed off, and the gases in the room are not perfectly mixed.  The region directly above the surface of the water has a very high concentration of H$_2$O vapor, and it is in this region that the evaporation/condensation equilibrium is maintained - until the boiling point is reached, that is.
A: The definition you quote is of open vessels,  i.e. there exists a liquid surface.On earth because of gravity it is a flat surface and the liquid is contained in a vessel.

My question is what exactly are we referring to as "pressure surrounding the liquid" with respect to a closed vessel. Does it mean pressure directly above the liquid surface or the pressure over the lid.

Lids are not in the definition, and the rise in pressure when a lid is on explains faster boiling  and how pressure cookers work.  Lots of diagrams here.

Pressure cooking is the process of cooking food under high pressure steam, employing water or a water-based cooking liquid, in a sealed vessel known as a pressure cooker. High pressure limits boiling, and permits cooking temperatures well above 100 °C (212 °F) to be reached.

A: Boiling is a phase change where a liquid changes to a gas. This is dependent on temperature and pressure. Unless it is sealed like in a pressure cooker, heated water is open to atmospheric pressure where vapor pressure will be equal to air pressure. At sea level air pressure is about 14.7 psi where water starts boiling at 100 degrees C. At higher altitudes where air pressure becomes less, the boiling temperature of water becomes less.
