What is the name of the cloth that Islamic women wear on their heads?

It is called a HIJAB. The Word hijab comes from the Arabic for veil and is used to describe the headscarves worn by Muslim women. These scarves come in a myriad of styles and colours. The type most commonly worn in the West is a square scarf that covers the head and neck but leaves the face clear. The al-amira is a two-piece veil.