Whilst the brain is a relatively small part of the body, percentage wise, it still demands about 20% of our daily calorie needs because it never stops working. Its only fuel, under normal circumstances, i.e. its fuel of choice, is glucose and your brain can’t store glucose (glycogen) like muscles do so it demands a constant supply.
That’s why if you don’t eat for long periods you become a bit fuzzy-headed and headachey and your brain drives you towards sweet foods. Additionally, if you chuck too much sugar into the system the brain gets a big grin on and goes “MORE PLEASE, NOW!”, which is not good as it makes you into a sugar burning maniac.
That doesn’t mean you should eat more sugar, no no no, but it’s another good reason not to cut carbs from the diet, carbs are chains of sugar and will provide brain fuel. The trick is to choose good quality carbs and to eat protein and fat alongside in order that those carbs are released into the bloodstream steadily.
If you’re a carb-shunner (trying to say that without showing too much derision!) then eventually your brain will learn to use ketones produced as a result of a high fat, high protein diet for about 50% of its energy needs and it has a couple of other fallback solutions under extreme circumstances. We’re not into extremes at fitnaturally though, we’re into balance and naturalness.