Water is a bunch individual molecules wiggling around. The hotter the temp, the greater the speed of the wiggles. If an individual molecule is below a certain speed (i.e. Temperature) then it doesn’t have enough speed to escape the electrical bonds drawing all the molecules together.
These molecules are constantly bumping into one another. Most of the time, it is a simple transfer of energy from one molecule to another. Sometimes multiple molecules hit a single molecule, causing that one to start to go faster. If the transfer of speed is enough, and that molecule is near the surface so it won’t immediately transfer its new energy away to others, it might have enough speed to escape the electrical attraction. This is why water evaporates. It is also why evaporation cools the water down, because some of its energy has left and those molecules that transfered their energy to the one that left are therefore much slower.
When you boil water, you are adding more energy to this mix, speeding up those molecules. The faster the whole thing is going, the more likely it is that double collisions happen, sending more and more molecules flying away. But, remember, the flying away molecules leave behind a cooler liquid because they are accumulating its energy, and then running away. That is why the pot of water doesn’t just all turn to vapor once you hit boiling point. It takes quite a while to boil all of it away because the more vapor leaving the pot, the cooler the remaining molecules are. Therefore you have to just keep adding more energy to the pot to keep it at that boiling point temperature.
So fundamentally, in the shower and in the pot, water is converting to water vapor for the same reasons. It just happen more quickly in the pot due to a greater average energy and the constant application of more energy to counteract the cooling effect.
Edit: I should also add that if doesn’t have to just be about probability of multiple collisions in the water in a pot example. The water near the heating element can turn quickly to vapor directly from whacking of the vibrating molecules in the heated pot. If it does this to enough molecules at once, they will rise up as vapor through the liquid, hence the bubbles.
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