The Yagnopaveetham is the triple stranded sacrificial strand of thread that is worn by those initiated into the Gayatri recital. The three strands represent the three sandhya rites that are to be performed when the sun rises and sets and when the sun is at the zenith. The rites are in adoration of the Hindu trinity (Trimurti): Brahma, Vishnu, and Shiva. The purpose of the rites is to invoke the Gods to bless the novitiate to lead a good life at all times (past, present, and future), in all places (heaven, earth, and nether region).
Each Strand represent that the barer of the thread has STUDIED ONE VEEDA OF THE TRAYI VEEDA PER STRAND VIZ RIG YAJUS SAAMA, (ATHARVA was not considered as a Veeda at that period of time)
A Brahmachari - vatu - wares three stranded one yajnopaveeta, in ancient times even women too were considered to have rights to ware and perform sandhya vandana. Later that her part of responsibility is shifted to her husband, since then Man after marriage ware a pair of yajnopaveeta, one for himself and another of his wife's. He has to perform all vidhis and give his wife her part of the punyaarjane.