Why do people cut back on kilo-calories?
The calorie is a unit of energy. Our body uses the energy found in food to create ATP (a molecule that is handy to deal with energy) with the help of oxygen (that we breath in). ATP can then be used for plenty of tasks such as importing ions through a cellular membrane or more ultimately walking, talking, warming up your body, etc...

Saying that some food contain 100 calories (not kilo-calories) does not mean that it will heat up 100 grammes of our body water by one degree (Celsius). It only means that we are ingested the same amount of energy than the one that is needed for warming up 100 grammes of water by 1 degree (Celsius).

You might to have a look at CrashCourse video on ATP and respiration.