Fleece is NOT just the woolly covering of a sheep or goat.  Fleece fabric is made from synthetic fiber. This material is generally very soft. It is can be manufactured from recycled plastic bottles or synthetic fibers, such as polyethylene . The fleece fabric is generally lightweight yet breathable, which means air can flow through it easily.  Learn more about breathable fabrics.

A lightweight, warm and soft fabric, fleece has some of wool's good qualities but weighs a fraction of the lightest available woolens. Polar fleece garments traditionally come in different thicknesses: micro, 100, 200, and 300, with 300 being the thickest and least flexible.

Polar fleece is a soft napped insulating fabric made from polyester. Polar fleece originated in Massachusetts in 1979 when Malden Mills, (now Polartec LLC), and Patagonia developed Synchilla (synthetic chinchilla).  It was a new, light, strong pile fabric meant to mimic, and in some ways surpass, wool. Company CEO Aaron Feuerstein intentionally declined to patent polar fleece, allowing the material to be produced cheaply and widely by many vendors, leading to the material's quick and wide acceptance.

You may also want to check out the women's microfleece clothing section.