Even when soil is shaded, water always attempts to move from areas of high humidity to areas of low humidity. A fully developed plant canopy keeps water that moves from moist soil to drier air trapped beneath the plants' leaves minimizing further evaporation, keeping soil moist and allowing roots to feed on dissolved soil nutrients, leading to enhanced plant growth.
Soil microbial life is constantly consuming soil organic matter (soil carbon) while breathing in oxygen present in the entrapped soil air. Microbes exhale CO2, which then moves from the soil to the atmosphere. A fully developed plant canopy keeps CO2 that moves from the soil to the atmosphere trapped beneath the plants' leaves where it is able to be taken in by the plants through the plant leaves' stomata, leading to further-enhanced plant growth.
The high concentration of moisture trapped beneath the plant canopy moderates the temperature between the soil surface and the underside of the plant leaves (making it warmer in the winder, cooler in the summer), which leads to a moderated soil temperature, which leads to a moderated plant root temperature and increased soil microbe activity, which lead to further-enhanced plant growth.