The chain of gold and black glass beads is known as 'Mangalsutra', a sacred thread  - a gift of the husband at the wedding to the wife, that she wears throughout her married life (like the ring in christian marriages). A
married Hindu lady can be recognized by the 'mangalsutra'. A lady without it, is either unmarried or widowed, or say divorced. 

Like the mangalsutra a married Hindu lady is supposed to have a vermilion mark, 'the kukum' on her forehead always, and bangles in her hands. If the husband dies, her vermilion mark is rubbed and the bangles are removed and the 'mangalsutra is taken out. It is considered very inauspicious to be seen  without a vermilion mark or bangles or the mangle sutra for a  married woman.

to get more information about an Indian marriage click here