The veil that some Muslim women wear is called a hijab. This veil covers the head and chest of the woman and is typically worn after a woman is past the age of puberty.
The hijab is to be worn by women when in the presence of men who are not part of their immediate family. So, when Muslim women are in public, they wear their hijab. While the word hijab is used to describe the veil, it is also used in reference to any piece of clothing that denotes modesty. It can even be used to refer to a women's behavior or demeanor.