Respiration is the process by which people (and other organisms) break down glucose (from sugars and charbohydrates in their food) in order to release energy. This process requires oxygen which we breath in.
Respiration occurs in almost every cell in the body because the whole body needs energy.
The energy is released in the form of a molecule called ATP which is easily broken down to provide energy when needed.
This energy can then be used for movement (muscle contractions) and other uses in the body, like making and transporting molecules.
Water and carbon dioxide (which we breath out) are also produced during respiration.
So, the chemical equation for resperation is:
glucose + oxygen --> water + carbon dioxide (+ energy)