The end goal of smoking brisket is to break-down meat collagens and connective tissues. In order to accomplish this, you need to smoke the brisket to an internal temperature at which point the collagens melt and the fibers separate.
However, certain cuts of meat like brisket can reach an internal temperature at which they plateau or "stall."
The stall itself is a result of what's called "porous bed free expansion cooling" - which is essentially evaporative cooling.
If you're from the western/south-western part of the United States, you might be familiar with a "swamp cooler" or "desert cooler" which uses moisture in order to cool the air.
A swamp cooler works by passing the warm outside air through a wet barrier - the water molecules on the surface evaporate which causes the air temperature inside the cooler to drop before being exhausted back into the air by a fan.
In terms of brisket, as the meat "sweats" it causes moisture to evaporate which cools the meat down. This concept is similar to human physiology - we sweat in order to cool our bodies down.
As the temperature of the cold meat continues to rise, the evaporation rate increases until the cooling effect essentially balances out the heat input. The meat will then stall or plateau until the all the moisture on the surface is gone.
The above is the reason that most of the bark formation occurs after the stall - this is an important realization as most people will wrap at the start of this process, rather than during it.
Learn more about when to wrap brisket here.
Brisket tends to stall at around 155 - 165F internally.
However, this number is dependent on the size of the brisket (can be 8 - 20 lbs), the type of pit you're using (airflow, water pan usage, fuel source), the moisture content (did you inject? what did you use for spices?) - even the accuracy of your thermometer matters.
The primary way to beat a brisket stall is through wrapping the meat - commonly referred to as a "Texas Crutch."
The Texas Crutch involves tightly wrapping meat in aluminum foil. Inside the wrap people also add a liquid like apple juice or even water.
The idea behind the liquid is that the moisture creates steam which further tenderizes the meat - liquids in general have a better heat carrying capacity than air (roughly 4.23x more) - which speeds up cooking.
Essentially, wrapping in foil prevents evaporative cooling; Any of the moisture that comes out of the meat combines with the liquid that you added to the wrap.
Keep in mind: A lot of beginners to barbecue will sort of be confused by the unwrapping part too. Essentially, people wrap until they beat the stall at 180-190F, they then unwrap the meat and put it back on the smoker to form a better bark. The problem is that the surface of the meat is now moist meaning both evaporation and cooling will happen. It's typically recommended to take the meat to your target temperature like 205F and then to unwrap - this is because it's likely that the meat will cool down to 180F or lower.
Another way to beat the stall is to increase the smoker temperature. People in barbecue are often told to smoke "low and slow" and then equate that to 225F. By increasing this temperature from 225 to 250-275F, or even 300F (called hot and fast), you reduce the chances of a stall even occurring.
Some smokers like pellet cookers and electric smokers are less likely to experience a brisket stall too. Electric smokers create a super tight seal which results in a humid environment. A pellet cooker creates a convection of heat which can further speed evaporation.
As with almost everything in barbecue, the opinions on wrapping are split; Either people like to wrap, or they don't. The people who do opt to wrap will use either aluminum foil, butcher paper, or both.
In a true Texas Crutch, the meat is wrapped in aluminum foil. Aluminum foil is an impermeable barrier and effectively prevents evaporative cooling from occuring. Depending on what's added to the wrap, you're essentially gently braising the meat.
A common issue you'll find with aluminum foil wrapped meats is that the trapped moisture produces soft, mushy bark.
Butcher paper functions in a similar way to aluminum foil in that you're wrapping the meat in order to prevent evaporative cooling.
The difference between the Butcher paper and the foil is that the butcher paper is a porous material and will readily absorb fat and water.
Wrapping with butcher paper results in less steam, meaning the bark isn't degraded as much.
The first time I heard of creating a "foil boat" for brisket was by Bradley Robinson (Chud's BBQ - actually an alumni of my Highschool - talk about a small world). He mentions in his video that he brought the method from Freedmen's BBQ to Leroy and Lewis.
In their iteration they only use foil to protect the edges of the brisket from drying out while the top of the brisket is allowed to form bark and to continue rendering fat. In this instance, the aluminum foil is used more for deflecting heat than it is for wrapping for the purpose of beating a stall.
Bradley does note though that the foil will collect meat juices and fat that essentially works to braise the meat - however, since he's foiling at around 175F (as I said above, several people wait into the stall) not much moisture is left at that point.
There have been other ideas proposed for wrapping brisket first in butcher paper and then foil boating. While I've tried the foil boat (I'm a big fan), I don't quite understand the added benefit of the paper.
I mean I know that tightly wrapping in butcher paper works but I don't really see a perceivable benefit of the foil at that point. Butcher paper already does a really good job of absorbing a lot of juices and protecting edges.
You also have the people in the camp of no-wrapping. All this entails is waiting for the stall to pass, which could take 1-7+ hours for a brisket.
Brisket stalling can be a super annoying part of the smoking process - especially if you're cooking for friends and family who eagerly await the meat.
Luckily, a number of things can be done to beat the stall and prevent evaporative cooling from ruining your day. Again, you can wrap in foil with a liquid, wrap tightly with butcher paper, foil boat, or simply wait out the stall and tell your friends/family that it's done when it's done.