Definition (answer s. str.)
"Low carb" usually means food that is low in starch and sugars.
Sugars are usually saccharose, glucose and fructose, although other sugars like maltose and mannose might be included as well.
Starch is food consisting of glucose chains, which means that your gut needs to break down the chains in order to take up the sugars.
Personally, I'd rather go with the glycemic index than with "carb" or "no-carb". Because the glycemic index (GI) measures the blood sugar spike each food causes. The higher the GI, the more insulin is produced by the pancreas, which in turn increases blood sugar. And the higher the blood sugar, the more sugar is turned into fat by the liver. Lists of the GI index are here or here or look for one here (note that with natural foods these values can differ, but as with counting carbohydrates, the principle is more important than the values themselves).
Beside that, the processing of food is often quite important as the food itself, for instance the GI of oranges is 43, but the GI for orange juice is 50 (source). That's because processing usually breaks down complex carbohydrate chains into simple sugars, that explains the high GI of baked potatoes. But it also makes inedible food edible, since raw potatoes are toxic and grass can't be digested, yet if you process the grass you will get a fine and very healthy powder.
Finally, food constituents are taken up differently by each person, depending on his digestive system, his gut flora, his metabolism, his enzymatic predisposition (= genetic predisposition), aso. For instance some people's liver can transform sugars better into fat than those of other people. These need to take up less calories.
If you watch it historically, you can see that the diets were developing from the "Montignac diet" in the 90-ties to the "Whole Food diet" during the millenia years and now the trendy "low-carb diet". Funnily enough, the Montignac diet was heavily (but wrongly) criticized by M.D.'s, the Whole Food diet is criticized by the Paleo diet people (due to the "anti-nutrients" in whole foods, who could have guessed that), and there will also soon be a movement against the low-carb diet, if it's not already veganism (note: Whey is not vegan). This all happened while the M.D. stuck to just counting calories, which is probably the most inferior of the diets discussed above, but will still lead to a similar outcome in the long run. The next movement will be the "genetic food" movement: You'll test your genes for a few hundred bucks and then they can recommend certain foods for you in order to loose weight.
In the end, you just need to find something that works for you, because there are several roads that lead to Rome. And if that road is just for you without any name on it, then that's still good.