In photosystem II, which is actually the first of the light reactions, H2O is an an input, and split. The H electrons and protons are used by the plant to create ATP for the Calvin cycle. As for the O2 molecules, they are released by the plant as waste. Which is good for us living organisms that require O2, which is required as the terminal electron acceptor at the very end of cellular respiration. The O2 that plants release into the atmosphere, is breathed in by us, and that is how it enters our body.
So the sugar from plants provides us chemical energy (we break it down over several steps and take the free energy to produce ATP).
The final step of cellular respiration, which is electron transport and oxidative phosphorylation requires those O's we inhaled, because it accepts electrons from NADH and FADH (which are both carriers of electrons from the glucose that has been broken down), and by accepting the electrons allows for H protons to enter the ATP synthase protein which phosphorylates ADP + Pi (inorganic phosphate) into ATP. This yields I believe 32-34 ATPs, by far the biggest energy making component of respiration. Those H protons that were used for oxidative phosphoylation then react with the Os and leave our body as H2O.
So in short, the products of photosynthesis that living organisms use are glucose and oxygen. The oxygen is crucial for organisms that use aerobic respiration (aerobic meaning they need O2).
I also forgot to mention CO2. CO2 enters the plant at the beginning of the Calvin Cycle. The plant uses carbon fixation, in which it basically takes inorganic CO2 from the air, and makes (fixes) it into an organic compound, glucose. This is actually how the plant obtains its biomass.
Anyway, without plants, our atmosphere would contain far too much CO2 to sustain life on earth. Think of Venus. It would act as a thick blanket that would retain all of the sun's heat, causing a runaway greenhouse effect.
