The Calvin Cycle is otherwise known as the light-independent part of photosynthesis. Here is what happens in stages:
1) Ribulose biphosphate (RuBP) is a 5 carbon molecules that binds to a molecule of CO2 with the help of the enzyme Rubisco. This would theoretically make a 6 carbon compound but this is a very unstable compound that breaks down instantly to form 2 3 carbon molecules called glycerate 3-phosphate (GP).
2) The 2 GP molecules are 'activated' by the use of an ATP molecule and are then reduced (due to the oxidation of NADPH to NADP) to 2 3 carbon molecules of triose phosphate (TP).
3) The 2 TP molecules then lose 1 carbon atom (between them) and this carbon atom can be used to synthesise sugars. The remaining 5 carbon atoms bond together and are phosphorylated by a molecule of ATP back into the 5 carbon RuBP molecule so the cycle can start again.
This means that every cycle produces one carbon atom. This means that 6 cycles are required to produce one molecules of glucose as glucose is a 6 carbon sugar. Note that this is why CO2 is in the overall equation for photosynthesis because the carbon from CO2 ultimately ends up in the sugars produced by the plant.