Several years ago I was working for a certain famous Idaho ski resort and living in company housing, where the drinking of alcohol was strictly prohibited. So of course, I was brewing in secret.
I was boiling my wort on the electric stove with an old copper pot I had bought at a yard sale and drinking beer. I was just to the point i had made my first hop addition when I turned around to get a beer. When I turned back around smoke was spewing out the bottom of the pot like someone had opened the doors to Morodor. The heat had melted a small hole in the bottom of my kettle.
I try to set my beer down on the table but knock it over, so it is draining on the floor, and grab the handle of the pot; pulling it off of the burner. Now, instead of smoke coming out from beneath the pot, there is wort pouring out from the pot and flowing on the burner, where it starts to smoke.
So I move the pot to the sink, while trying not to spill boiling wort on myself, but succeed in spraying hot wort all over the kitchen counter and cabinets.
As my precious wort drained away I am using the mop to try to clean the top of the stove off before it catches on fire. To make matters worse, the fire alarm was going off. Luckily I was the only one home but some of the buildings at this particular resort were hardwired into the central fire alert system. It turned out they had never bothered to hook my building up to it so that avoided some awkward questions.
Stupid yard sale pots anyway.
One constant in brewing, no matter what kind of beer you brew, is the boil. Beer should be boiled vigorously for at least an hour. This doesn't have to be so hot it is jumping out of the kettle or so light the surface is just barely moving; just a nice rolling boil with the lid off.
There is a lot going on during the boil, which is why it is not something you should ignore or take for granted. The big things is your wort is becoming sterile.
Despite what you may wish there is yeast and bacteria living in your tap water, just not in quantities if can hurt the human body. Also, in order for a bacteria to make you sick it has to survive the stomach acid and white blood cells fighting it. If you add the same bacteria cell to your wort it will be an environment with nearly unlimited food and perfect conditions for growth. If you don't have a pot big enough for a full volume boil, boil some water ahead of time and then set it aside covered. One of the first things a notice brewer can do to greatly improve their beer is making a full volume boil.
Besides sanitation there is other, science, stuff going on; proteins are forming, hop oils are isomerising, sugars are caramelizing and water is evaporating.
Many malts, especially pils malt, contain high levels of dimethyl sulfides, or DMS, which will contribute a vegetative or creamed corn flavor to your beer, which you probably don't want. The DMS will mostly boil out if you leave the lid off during the boil.
If you have brewed at least one batch of beer you have had a boilover. You will meticulously watch your boiling wort for 20 minutes and then blink and your beer will gleefully leap from the pot onto the stove. When you add hops your wort will boil over. If you are brewing on a windy day the wind will eddy a little and your beer will boil over.
There are a couple of ways to keep from getting a boilover. The simplest is just buying a bigger pot. John Palmer, in How to Brew, suggests putting some stainless steal nuts in your pot.
I just try to keep a close eye on my pot, which results in me boiling over about every 3rd brew day.
Saying a brewer needs to master the boiling of water seems redundant, and not very sexy, but getting a nice boil is critical to producing good beer.