Pilling can occur in your fleece and wool fabrics. It happens when pieces of the fabric pull away from the garment and collect together in tiny clumps on its exterior in a noticeable manner. It typically happens when there is friction between the piece of clothing and another item, like a backpack or an outer shell layer.
It can also occur with frequent or rough washing, use or handling. However, your vest can recover from pilling. A pill shaver or sweater stone, which can be purchased in many stores and online to remove those excess small balls of fabric that have worked themselves up in a most unappealing way on your favorite vest. In the future, wash and dry carefully as described above.