The yellow thread like structures in the white saffron flowers form the the saffron or kesar, which is a spice and used in different ways in India or abroad.
It is used as additive in food because it renders a beautiful colour and a distinct flavor to it. Saffron is also used in medicine and beauty products. Here in India it is considered sacred and is used to tilak deities as well as the devotees. Saffron has been a part of our lives since many a generations.