The most basic definition of waist training is the process of using a steel boned corset to modify your waist into an hourglass shape with semi-permanent results.
Steel boned corsets are worn for many reasons and situations. Some people wear them as a fashion statement, while others wear under clothing for back and posture support. However, many women are looking for that classic hourglass figure to really turn heads at a special event. It has nothing to do with losing weight, spot reducing or doing ab exercises while wearing a waist cincher. The hourglass figure is attained as a result of the moving of floating ribs and the reduction of space in the abdomen.
Weight loss tends to happen mainly because the corset also acts as an external LAP band, not allowing you to eat large quantities while wearing the corset.
We tend to refer to the current trend of latex "waist trainers" (yes, the Kim Kardashian variety) as "waist taming", as there is no way to truly cinch them and even the firmest latex can't compare to stainless steel bones.