Your blood pH should be in a specific range. CO2 dissolved in your blood makes it more acidic. When you hyperventilate, the concentration of CO2 in your blood drops. When you breathe into a paper bag, you inhale more CO2 than you would just breathing air from outside the bag, and it helps compensate for the extra CO2 you're exhaling.

IMPORTANT

BREATHING INTO A PAPER BAG IS ONLY USEFUL FOR CERTAIN CAUSES OF HYPERVENTILATION—FOR OTHERS, IT CAN MAKE THE SITUATION WORSE!

basically, carbon dioxide as a waste product that, when dissolved in the blood, makes it more acidic. when someone is blowing off too much carbon dioxide but is otherwise physically healthy, for example during to an anxiety attack, breathing into a paper bag helps to recoup some of that carbon dioxide, thereby keeping their blood from getting too basic. this important because everything in our body works best within a really very narrow pH range, as all of our body’s functions are optimised for that range and may work poorly or even not at all out of it.

IF, however, a person is hyperventilating as compensation for their blood being too acidic, such as with kidney problems or certain toxic substances, breathing into a paper bag is a HUGE mistake, as it interferes with the lungs trying to fix the acidity as best as they can!

another reason for hyperventilation is low oxygen levels in blood, even when CO2 may be normal or high. this can be do to a very wide range of things—there’s no one sign that’s guaranteed to always be there—but you may notice they are blue or grayish around the edges, especially around the lips and nails. it goes without saying that these people also should not be made to rebreathe from a paper bag, since they’re gasping for more oxygen, not trying to blow off more carbon dioxide.

that’s why it’s really very important to have a good idea of why someone is hyperventilating before trying to treat it. even in case of anxiety attacks, unless they’re common and the person having them is aware of what’s going on, rather than giving them a paper bag, it’s better to have them: sit or lay down, ideally with the head level with the heart and help them through breathing/mindfulness exercises. sometimes one kind of hyperventilation masks itself as another, so without the ability to check blood tests, better safe than sorry 💕

The resistance to exhaling and inhaling adds more rhythm to your breathing. Hyperventilation is you breathing in and out too fast, leading to bad gas exchange. The bag forces you to breathe slower. The bag doesn't actually do anything more, than someone looking in to your eyes, and commanding you to "inhale... exhale.... inhale... exhale..."

This is why people with panic disorders (like me), are taught some breathing rhythm thing we can exercise. I myself use "breathe only through the nose and fully exhale and inhale" (Harder than you think, and I played the french horn and tuba for +10 years - I got good capacity). Full inahle and exhale also activates you parasymphatic nervous system and calms you down.

It is just about the feeling of gaining control, giving you something to focus on that keeps you present.

The bag tricks isn't even recommended anymore, since people forgot that they'd actually also need to breathe oxygen in. Leading them to be more likely to pass out from lack of oxygen. Also doesn't actually teach you methods. of controlling your emotions, but instead forcing you to rely to a tool. And if you don't have that tool to get comfort and control from, it makes things worse.

As another comment correctly pointed out, hyperventilation lowers your blood CO2 levels below normal/healthy thresholds, and the intent of paper bag rebreathing is to slow your breathing, and have you breathe in less oxygen-rich air/previously exhaled CO2. While the mechanism of:

>hyperventilation -> low blood CO2 -> increase blood CO2 -> alleviate hyperventilation

is well accepted, I don't believe that there is robust science supporting paper bag rebreathing specifically.

Additionally, paper bag rebreathing can kill people who are sensitive to hypoxia (lack of/low oxygen) and people who are suffering medical emergencies that appear like anxiety attacks but aren't (commonly heat attacks). AFAIK, the current recommendation is to coach people through their breathing, and to have them breath through pursed lips. While paper bag rebreathing should be fine for otherwise healthy people, there's not really a reason to use a method that could be dangerous when there are less/non-dangerous methods available.

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People providing information that could be taken as medical advice (even if not so intended), should have medical credentials and should state them in their post. Most legitimate experts will also understand that the whole context of a person’s clinical presentation has to be considered as the same symptom can occur for different reasons. An expert will usually not say, “this is the only correct answer.”

I cannot speak to the physiological aspects of this at all, but I can say that someone who is hyperventilating may need medical attention. Other commenters have also suggested that bag breathing can be dangerous in some circumstances.

PLEASE NOTE that if someone is having a panic attack and they are not hyperventilating, DO NOT give them a bag to breathe into as this will exacerbate their symptoms. Increased CO2 inhalation has been found to correlate with worsened symptoms in individuals experiencing acute anxiety. CO2 enriched air will actually cause anxiety in otherwise healthy people, and is sometimes used in research studies for the purpose of inducing anxiety.

To be clear: I am not saying that someone who is having a panic attack and is hyperventilating can be given a bag to breath into. I can only comment on the often mistaken assumption that bag breathing is the appropriate treatment for a panic attack. Again, please always refer to medical professionals.

Source: https://www.nature.com/articles/s41398-019-0634-z

And I am a graduate student in clinical social work.

Edited: for clarity.

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It doesn't actually do anything other than make someone pay attention to their breathing. These days first aid training recommends things like counting on your fingers or putting your hand on your tummy and trying to lift it with your breath, not least because no one has paper bags handy anymore.

The paper bag is just something for the person to focus on inflating/deflating to help them take slower/deeper breaths.