There are effectively 3 stages to this process:
1) Carbon dioxide fixationThis process is called fixation because carbon dioxide from the air is converted into an organic compound which cannot move away.
It is probably convenient to consider 6 molecules of carbon dioxide entering the cycle, so that the next step below occurs 6 times.
Carbon dioxide reacts with ribulose bisphosphate RuBP.
For this reason RuBP is called a CO2 acceptor.
Yet another way of saying this is that RuBP is carboxylated.
This occurs under the influence of the enzyme ribulose bisphosphate carboxylase (RUBISCO) which is said to be the most abundant protein on the planet.
Ribulose bisphosphate has 5 carbon atoms and 2 phosphate groups, and by accepting one more carbon atom from CO2 it should be converted into a 6 carbon, 2 phosphate compound. However ...
This compound is immediately converted into 2 molecules of glycerate 3-phosphate (GP), which contains 3 carbons and one phosphate group.
For every 6 molecules of CO2 entering the cycle, 12 molecules of GP are produced.
This pathway is called C3 carbon fixation because the first product is a 3-carbon compound. Some plants have an alternative pathway - C4 carbon fixation - in which the 4-carbon compound oxalacetate (OAA) is produced and others have a CAM pathway.
2) Carbon dioxide reductionThere are several published versions of this section, varying in complexity, and using different terminology.
This stage is so called because when CO2 reacts with H from reduced NADP it gains hydrogen and loses oxygen to become CH2O, the empirical (simplest) formula for carbohydrates. Reduction is loss of oxygen, or reaction with hydrogen, or gain of electrons. However the CO2 is now part of glycerate 3-phosphate (GP).
Glycerate 3-phosphate (GP) is converted into triose phosphate (TP) using reduced NADP and ATP.
The reduced NADP provides the reducing power (hydrogen) and is converted back to NADP which is then reduced again in the light-dependent reactions.
ATP is also used to provide energy for the conversion. It is converted into ADP + Pi, which are reconverted into ATP in the light-dependent reactions.
Some of the triose phosphate (two molecules out of the twelve) is removed from the cycle, to be converted into glucose, or other molecules such as starch, lipid or protein.
3) Ribulose bisphosphate regenerationIn a complex series of reactions, the remaining ten molecules of TP are converted into 6 molecules of the 5-carbon compound ribulose monophosphate
(10x3C=6x5C, but some phosphates are lost from the cycle).
Ribulose monophosphate is converted into ribulose bisphosphate, using a phosphate group from ATP.
Ribulose bisphosphate reacts with/accepts carbon dioxide/becomes carboxylated, to keep the cycle operating again ...