How does boiling work? Let's assume that the exact boiling point of water is 100 degrees. Now I have a stovetop and a pot. I add the water to the pot, put it on the stovetop and turn the temperature to exactly 100 degrees. Now what will happen? There's no additional energy flow since there's no temperature difference between the stovetop and the pot right, but the water is already at 100 degrees at it's boiling point so it should boil, but it somehow doesn't. Can you explain this to me? Do we need to keep the stovetop above 100° for water to start boiling?
Edit:
Since my question is being misinterpreted here's what I mean.
Consider a pot on a stovetop filled with liquid water. Put another cup which can float on top of it in the pot and fill it with water as well. Now turn the stove top so the water in the pot starts boiling. The water in the cup though will not boil while water around it does even though they are at the same temperature 100°C. My conclusion is that you need additional heat rather than the one that just keeps the temperature at 100°C to actually make the water boil, which the cup does not get since all the additional heat from the stovetop is being used to transform the water to a gaseous state in the pot. From this then I can conclude that the stovetop must provide additional energy other then the one that keeps the water at 100°C to make it boil, the stovetop therefore must be at a greater temperature then the liquids boiling point (so greater than 100°C, the assumed boiling point)and cant be just at 100°C. Now why then is this the case. Why do we need that extra energy if the water is already at 100°C which is said to be the temperature at which water boils at normal pressure, if then we can reach the boiling point without the water boiling in the example I gave.
 A: 
put it on the stovetop and turn the temperature to exactly 100 degrees. Now what will happen?

The stove is only hot on one side.  If the surface were exactly 100, then the pot would rapidly lose heat to the environment and cool down.  Heat would flow from the stove to the pot, but never bring the water to 100.  No boiling.
You could instead set the pot inside an oven that maintains 100C.  In that case the pot and water would also maintain 100.  If the air were not saturated, it would evaporate until the saturation point were reached.

the water is already at 100 degrees at it's boiling point so it should boil

Water at atmospheric temperature boils doesn't boil because it's 100C, it boils because energy is being delivered to the water faster than it is being dissipated by other cooling methods
When less than 100C, this excess energy increases the temperature of the water.  When at 100C, this excess energy drives the phase change in some of the water.

Here's another way to think of it.  A dam operator tells you that the local reservoir overflows when it reaches a reference height of 100m.  You walk over to the dam and see that although the water is currently at a height of 100m, there is no water overflowing.  The gates are completely dry.
The operator tells you that it's not so much that it overflows when it's exactly at 100m, it's that it overflows if any more water comes in when it's at the 100m mark.  The overflow removes water so that the height doesn't go up.
This is what's happening in your scenario.  The water doesn't boil just because it's 100C, the water boils when it's at 100C and additional thermal energy is added.  The boiling removes energy so that the temperature stays 100C.  But in our everyday experience, we never have water just sitting at 100C and being static.  Instead we have it on a stove where lots of energy is being added, so the boiling is constant.
A: The temperature at which a phase change happens is usually bidirectional—this is not just the temperature at which liquid water becomes water vapor, it is also the temperature at which water vapor condenses back to liquid water.
And so a better way to think of it is, this is the rare temperature at which water doesn't care which form it takes. At higher temperatures, water prefers to be vapor. At lower temperatures, water prefers to be liquid. In the middle, at this one particular temperature, water could go either way.
The real world is unfortunately more complicated than this simple model. If you were to run this experiment, you would see something that you might call “boiling”... But it would not be the “rolling boil” that you look for in, say, pasta. What is happening is that water actually contains air dissolved in it, it actually makes the water taste better, your taste buds can pick up on it. (It can even make coffee taste less bitter, which was only discovered recently and has led to a bunch of “nitro cold brews” at coffee shops.) As the water gets hotter, it loses its ability to dissolve this air and the air precipitates out as bubbles.
Similarly, you would notice that if you left this pot there for an hour, even though it never goes above the boiling point, the water is disappearing. You would notice this even at a low temperature but it becomes more visible at higher temperature. What's happening there is that the air has an ability to dissolve a certain amount of water. And unless the air is saturated and condensing on your cold windows and mirrors, fogging them up, the heat is encouraging the water to dissolve into the air in a couple of different ways. So you will see a sort of mist coming up off of this nearly boiling but not quite boiling mixture. This also removes heat from the pot, so if you were to check the temperature of the pot very carefully, you discover that the pot of water never actually reaches the temperature of the stove.
A: The question proposes the following observation: a cup containing water is floating in the water contained in a larger pot, and when the larger pot of water boils, the water in the cup does not.
I have not repeated the above experiment, but I think it is credible and I am guessing the answer is as follows. When the pot of water is observed to be "boiling" the water in contact with the cup is close to 100 degrees celcius (the boiling point) but the water in the cup is a tiny bit cooler because the thermal conductivity of the cup, and of water itself, is not infinite. The air above the water in the cup is cooler still. So the temperatures are 100 in the pot, a little less in the cup, and less still in the air just above the cup. So there is heat flow, but it never quite brings the water in the cup to boiling point.
To test the above one could use accurate thermometers. One could also try using instead of a cup, a small metal container or tube with only a small opening, and make it almost entirely submerged in the pot of water, and make sure the pot of water is not just beginning to boil at the bottom or the edges but is boiling right through, in a "rolling boil".
Another thing to watch out for is impurities such as salt. These can easily change the boiling point by several degrees.
A: Boiling point is something we call as the point at which the vapour pressure is equal to the atmospheric pressure. Boiling happens when the vapour pressure is very very slightly greater than the atmospheric pressure this happens because the water (in this specific case) bubbles gets filled with the water vapour and if the vapour pressure is greater than the atmospheric pressure then the bubble starts to become larger and suddenly gets ruptured, at that point of time we call it as the water is boiling.
If the pot is on the stove but no heat transfer from the stovetop to the pot its still 100 degrees but it won't boil because for boiling we require some amount of energy to get converted into the kinetic energy of molecules of vapour, it's still there but not enough to fill the bubble and to make it larger. But if suddenly we increase the temperature of stovetop (in other words create temperature difference between the stovetop and the water already at 100 degrees), the water in the pot on the stove will start boiling since there is heat transfer between the stovetop and the pot, then the remaining amount of energy coming from the stove will get more and more converted into the kinetic energy of the molecules rather than increasing the temperature of water and that amount of kinetic energy will be enough to form a bubble and make it rupture as well, and hence we see boiling phenomenon.
