It is believed that not only do mantillas help one's humility towards God in a physical way, but also in a spiritual manner. When a lady is veiled she is more inclined to feel directed towards everything holy. This piece of material enshrouds her and she is able for that hour or so to leave her earthly thoughts behind and set her eyes upon Heaven.
The mantilla helps to concentrate on the sacred.
Heart upon God.
Praying at Holy Mass unaware of her surroundings.