When you eat less than 50 grams of carbs a day, your body eventually runs out of fuel (blood sugar) it can use quickly. This typically takes 3 to 4 days. Then you’ll start to break down protein and fat for energy, which can make you lose weight. This is called ketosis. It's important to note that the ketogenic diet is a short term diet that's focussed on weight loss rather than the pursuit of health benefits. 
There is a reason why we store hundreds of thousands of calories in the form of fat in our body and only about 2000 calories in the form of glucose (with only a small amount of this useable by the brain). The reason is simple - The body prefers fat as its fuel source. Mark Sisson explains this in his article ‘A metabolic Paradigm Shift, or Why Fat is the Preferred Fuel for Human Consumption’. 

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On a ketogenic diet, your entire body switches its fuel supply to run mostly on fat, burning fat 24-7. When insulin levels become very low, fat burning can increase dramatically. It becomes easier to access your fat stores to burn them off. This is great if you’re trying to lose weight, but there are also other less obvious benefits, such as less hunger and a steady supply of energy. This may help keep you alert and focused.
Children who discontinue the diet after achieving seizure freedom have about a 20% risk of seizures returning. The length of time until recurrence is highly variable, but averages two years. This risk of recurrence compares with 10% for resective surgery (where part of the brain is removed) and 30–50% for anticonvulsant therapy. Of those who have a recurrence, just over half can regain freedom from seizures either with anticonvulsants or by returning to the ketogenic diet. Recurrence is more likely if, despite seizure freedom, an electroencephalogram shows epileptiform spikes, which indicate epileptic activity in the brain but are below the level that will cause a seizure. Recurrence is also likely if an MRI scan shows focal abnormalities (for example, as in children with tuberous sclerosis). Such children may remain on the diet longer than average, and children with tuberous sclerosis who achieve seizure freedom could remain on the ketogenic diet indefinitely.[46] 

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