Why does a magnesium ribbon continue to burn when it is placed in a jar , full of CO2 ? If your answer is that CO2 decomposes into carbon and oxygen ,then please tell that why does it happen only in case of magnesium and not in wood ?

Magnesium burns in the presence of many gasses, carbon dioxide being just one of them. You are correct that the carbon dioxide splits into it's primary components of carbon and oxygen. This type of reaction is called a decomposition reaction, and only occurs in the presence of extreme heat, as this energy is needed to break the bonds between the atoms of the carbon dioxide.
The reason that this does not occur with a wood fire is simple; wood fires are very low in heat. A magnesium fire is many times hotter than a wood fire. While a wood fire with bellows and a stack can reach 1100 degrees Celsius, a small pile of magnesium shavings can easily pass 3000 degrees Celsius as it burns.
This property is useful in devices like flares, as that allows the device to work in many places, even underwater, as the magnesium decomposes the water into oxygen and hydrogen.