Aerobic means "with oxygen" and Anaerobic means "without oxygen". Anaerobic exercise is the type where you get out of breath in just a few moments, like when you lift weights for improving strength, when you sprit, or when you climb a long flight of stairs.
and Aerobes refers to organisms that require oxygen for their metabollic activities.
Anaerobes are organisms that do not require oxygen for their metabollic activities.
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Respiration is the process of releasing energy from the breakdown of glucose. Respiration takes place in every living cell, all of the time and all cells need to respire in order to produce the energy that they require.   There are two main types of respiration, aerobic and anaerobic.   ·     

Aerobic respiration is the respiration where glucose is broken down by oxygen to release energy with carbon dioxide and water being produced as by-products of the reaction. 

    Glucose + Oxygen  Carbon dioxide + Water + Energy

Anaerobic respiration is the respiration which occurs in the absence of oxygen to produce the energy.
  Lactic acid + Energy (in animals)
                             ,                Glucose Ethanol + Carbon dioxide + Energy (In plants)