Question: To my knowledge, bypass air produces 80% of total thrust. But I don't understand to how it does that. By accelerating the air, by increasing the speed or increasing the pressure of the air? Is it doing this by Bernoulli's principle or something like that?

Answer: 
The bypass air is accelerated by the fan at the front of the turbofan engine. This changes its velocity and therefore its momentum, which is the definition of a force (in this case: thrust):

$$ F = \frac{\text{d}}{\text{d}t} p = m \frac{\text{d}}{\text{d}t} v = m \cdot a $$

This thrust contributes to the total thrust of the engine. How much will depend on the bypass ratio of the engine and other parameters, but 80% is plausible for a high bypass turbofan. Bernoulli's principle has nothing to do with this.

You can see the accelerated airflow in the following animation:

[![Turbofan airflow](https://i.stack.imgur.com/0fvyl.gif)](https://i.stack.imgur.com/0fvyl.gif)  

(source: [Wikimedia](https://en.wikipedia.org/wiki/File:Turbofan3_Labelled.gif))

The air coming from the engine core will move even faster, but there is less of it in a high bypass turbofan resulting in less total thrust coming from the core:

> 
> The fan airflow, referred to as the cold air stream, is accelerated by the fan and passes through the engine remaining outside of the engine core. The cold air stream moves much slower than the hot stream gas flow passing through the engine core.
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([skybrary.aero](https://www.skybrary.aero/index.php/Turbofan_Engine))
It doesn't bypass *everything*, just the combustion chamber. **Notably, the air still goes through a fan**.

High-bypass turbofan engines make most of their thrust from the ducted fan. Very much like a turboprop except the blades are smaller and enclosed by the cowling.

@Harper's answer on [What is the difference between turbojet and turbofan engines?](https://aviation.stackexchange.com/questions/71301/what-is-the-difference-between-turbojet-and-turbofan-engines/71314#71314) explains that nicely: a high-bypass turbofan extracts most of the exhaust energy from the jet part and uses it to spin the fan, instead of exhausting really high speed air from the jet part directly.

Low-bypass turbofans have a mix of thrust from fan + jet, while a pure turbojet has zero bypass, just compressor blades and no fan.