Each pokemon belongs to a specific type as well as the moves they can learn. Different types have their own specific strengths and weaknesses over the other. Knowing the relationship between these types is vital in Pokemon battles and encounters, adding depth to the strategy. If you wish to become a Pokemon champion, it is imperative to have more than enough information about you and your opponent's pokemon's strengths or weaknesses.
You can download the original PDF of this chart from the official Pokemon X/Y site