Your brain does what it does thanks to a cell type called a
neuron. These neurons, which are hyper-connected to each other, are
responsible for how information travels throughout the brain in the form of electrical signals.
Neurons creating and carrying these electrical signals from one part of the brain to another
require a process of keeping charged particles separated from each other at different concentration levels: an electrical gradient.
This electrical gradient is created by
a pump (the sodium-potassium pump) which pushes 2 potassium particles inside and 3 sodium particles outside the neuron’s cell wall each time it pumps.
Like a water pump that pushes water to move upwards against the natural tendency for it to flow downstream (thanks gravity!), running this electrical gradient pump to keep particles separated by a cell wall when
they naturally want to come back together (thanks
diffusion!) requires a very large amount of energy.
To power this pump, neurons (and most other cells in your body) use an energy storage unit called
ATP (think of these as battery packs that get used up, re-charged, used, and so on).
A steady supply of oxygen is needed in order to constantly recharge ATPs so their energy can be used to power the pump, which enables neurons to do their job of carrying electrical signals, which enables the brain to be, well, brain-like.
These neurons, in maintaining these gradients to send electrical signals around, use up so much energy that your brain needs 20% of your body’s total oxygen supply even though it only makes up 2% of your body’s total weight. Just 3-4 minutes without oxygen can lead to brain injury.
TL;DR: The brain is made up of neurons, which need constant electrical gradients to do their job of carrying electrical signals around the brain. Pumps within the neuron create and keep up this electrical gradient. Recharging the cell's batteries to power these pumps needs a very large and steady amount of oxygen, more than any other place in your body.