Why/how do plants both respire and photosynthesise?

First of all, respiration is not breathing. Respiration is combining oxygen and glucose to form energy (ATP) with carbon dioxide as a waste product. All living things respire in order to obtain energy to carry out basic cellular functions, and therefore plants must respire. However, plants also photosynthesise - wherein carbon dioxide from the atmosphere is combined with water by the plant and using sunlight produces glucose (used for plant growth) and oxygen. It is the opposite reaction to respiration.