Very simply Ketones are organic chemical compounds that your brain, heart and muscles can use as a fuel source for your mitochodria to produce energy. Ketones are made in your liver but can be taken as a supplement which increases available ketones for use by the body in the absence of glucose. Ketones may well be the primary fuel source that your body used throughout our evolution in the absence of excessive glucose. If you think about it we have only really had freely available glucose in our diets in the last 100 yrs where we have seen consumption per person per year multiply 100 fold in the west.
The way I explain it to my clients is that its a bit like comparing burning petrol for fuel (glucose) and burning logs (ketones). Petrol is easy to light and burns impressively but it soon burns out and you require more to keep you going. Logs are harder to light but burn longer and don't create as many nasty combustion products as petrol (the end products of using excessive glucose as a fuel are called AGEs : Advanced Glycation End-products http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3704564/).
The probable benefits of switching your body to a ketone currency (increasing available ketones and decreasing glucose) are :
Suppression of appetite which can help you loose weight
Improved athletic performance
Improved cognition (your brain loves ketones)
Neuroprotective effect - ketones may protect the brain from age related degeneration
Anti-carcinogenic effects (in mice at least) as cancer cells cannot use ketones well and it seems to promote cancer cell death
Some anti-inflammatory properties have also been observed
The negatives associated with a ketogenic approach are:
Possible bad breath in Ketosis
If you take too much MCT oil (Medium Chain Triglyceride oil made from coconut and palm oils - the C8 Caprylic Acid form would seem to be the best at promoting ketones) can cause disaster pants (unexpected improved transit of the contents of your bowels). Powdered forms of MCT are available and seem to be even better at promoting ketones but currently are expensive.
Personally I use Bulletproof coffee with added MCT oil in the morning to provide my exogenous ketones (fatty coffee - no carbs)
For more information you can listen to various podcasts by Dominic D'Agostino