The Calvin cycle depends on light reactions because they power the electron transport necessary to produce ATP, which in turn powers the Calvin cycle. The Calvin cycle is the major method by which plants and algae produce carbohydrates and oxygen from water and carbon dioxide. It is thus one of the most important chemical cycles in nature as the basis of nearly every food chain.
As explained in "Molecular Biology of the Cell" on the National Center for Biotechnology Information website, the light reactions of photosynthesis are the chemical changes in chlorophyll caused by the absorption of light. Chlorophyll is a carbon-based molecule of great complexity surrounding a single magnesium atom. When the chlorophyll molecule absorbs light, its increased energy causes the magnesium atom, with its low electronegativity, to release electrons, which are then transferred to other molecules powering the creation of both ATP and NADPH, crucial molecules for the Calvin cycle and other energetic processes of the cell.
The Calvin cycle uses nine ATP molecules and six NADPH molecules, which it then uses to help create a series of different compounds from carbon dioxide, water and existing catalysts. Each different compound used before the creation of a carbohydrate takes less energy than a direct transformation, meaning that it is easier to create the carbohydrate using these several steps than it is to create it all at once.