I'll let wikipedia do the job
C3
C3 carbon fixation - Wikipedia, the free encyclopedia
Photorespiration
Photorespiration - Wikipedia, the free encyclopedia
Take home message is that C3(Beans, Bananas, Rice) plants fix carbon for photosynthesis using a a 3-carbon sugar while C4(Sugarcane, Maize, Sorghum) plants use a 4-carbon sugar. Yet another type of carbon fixation would be CAM(Pineapple, Agave, Cactus) Photorespiration is bad because it uses carbon dioxide in a way that does not make the plant grow.