Benign ketosis is a state induced by low carbohydrate diets, where the body burns fat as its main source of fuel rather than using carbs, which are usually stored initially in the muscles as a substance known as glycogen. It is called benign ketosis because it is a safe and healthy condition, rather than ketosis experienced by diabetics, which is not benign.
As the body burns fat, it produces a byproduct called ketones. Ketones are released out of the body through the urine and through the lungs. Ketones are the reason why one of the most documented side effects of the Atkins diet is that it can make people's breath smell a bit strange – the ketones have a sweet smell, almost like pear drops, which is occasionally noticeable on the breath (it is not a disgusting smell like general "bad breath", but it can be strong – sugarfree gum or a strong minty mouthwash will generally mask it).
Some degree of benign ketosis has to occur for the low carb diet to work, as it shows that the body is running off of fat. It will normally be induced within the first three days of following a low carb diet, as the body will at this point have used up any remaining glycogen reserves and switched to burning fat instead.
Testing for the presence of ketones is the best way to see if the Atkins (or other low carb diet) has taken effect, and to what degree you are experiencing ketosis.
Ketosis testing sticks, often called Ketostix, are available from most pharmacies. They are generally used by diabetics to check for the non benign kind of ketosis which can accompany their condition. If you are following a low carb diet, it can be a good aide to buy a pack of the testing sticks to help you see when you go into ketosis, and how strongly ketosis is taking place. The sticks are cheap to buy, and usually come in packs of 120. You can buy Ketostix over the counter.
To test for ketones, simple pee on one of the testing sticks (much like doing a pregnancy test). If Ketosis is not taking place, nothing will happen, but if it is, the stick will turn a range of colors from pale pink, showing the presence of traces of ketones, to a very dark purple, showing deep ketosis. There is a chart on the pack of Ketostix to show you the different colors and the quantity of ketones this represents (though bear in mind the packaging is designed for diabetics, so it will tell you that the darker the strip goes, the more dangerous it is – as your ketosis is the benign kind, actually the darker it is, the better your diet is working).
You may like to experiment by testing at different times, you will see that after exercise, the sticks are prone to go much darker, as fat has been burnt, producing ketones, as you were working out.