Photosynthesis is the process by which plants convert light energy into chemical energy that can be stored in the plant for latter use. The energy is stored in carbohydrates, that are synthesized from carbon dioxide and water, releasing oxygen as a by-product.
The basic chemical reaction is : CO2+H2O+light=CH2O+O2 Where CH2O is a carbohydrate. Actual reactions involve a number of CO2 and H2O molecules.
In a Martian settlement, photosynthesis is required for food production, and is also a part of the Carbon cycle. In this cycle, carbon, as CO2, is released in the settlement atmosphere by combustion of carbohydrates and other carbon molecules (food) in lifeforms, and extracted from the atmosphere by the photosynthesis process. An equilibrium between CO2 production and absorption is required to keep the atmosphere breathable. Extra carbon is stored in carbon sinks, such as plant structures, methane gases and lifeforms.
If required, the natural carbon cycle can be partially replaced/supported by CO2 extraction and carbon storage in methane using the Sabatier process. The synthesis of carbohydrates, however, must still be done using biological reactors such as bacteria.