Light intensity, carbon dioxide concentration, temperature and also the amount of chlorophyll.
Why does temperature affect photosynthesis
Photosynthesis is a process that uses enzymes. If the enzymes get warmer, photosynthesis happens at a faster rate, but if the enzymes get too hot, they will denature and photosynthesis will stop.
What other organisms photosynthesise?
Algae (pondweed and seaweed), as well as some bacteria. If there is a chloroplast, it will absorb light energy and photosynthesise.
Why do we care about the rate of photosynthesis
Anyone producing food crops will want to maximise profit. Adding lighting, carbon dioxide or heat into a greenhouse/glasshouse will give faster growth but may cost more, so may not be worth doing.