Rayon is a breathable fiber. Rayon fabrics used in clothing are generally breathable, but there is no guarantee that every finished rayon fabric will have this property. This is because there are other factors besides fiber content that can affect the breathability of the finished fabric.
In the context of clothing or sewing materials, breathable fabric is a fabric that allows air and moisture to escape through it. These properties help ensure wearer comfort through evaporative cooling. Sweat travels through the fabric and evaporates, providing a cooling effect.
Some breathable fabrics absorb moisture easily. Typically, breathable fabrics absorb moisture or wick it away. Some breathable fabrics can do both to varying degrees, but the fabric doesn't necessarily have to do both in order to breathe effectively.
Manufacturers take natural raw materials such as bamboo, wood chips, or wood pulp and process them with various chemicals to derive rayon fibers. The resulting rayon fibers are naturally breathable. At each step of the manufacturing process, manufacturers make a choice to either increase the breathability of the fibers or reduce their breathability. These choices will depend on the intended end use of the finished fabric.
Rayon has many possible industrial applications. In addition to apparel fabrics, manufacturers use rayon to produce upholstery fabrics, tire components, upholstery, and a variety of other products. In finished rayon for these other applications, breathability is not an important consideration.