She possibly originated as a Vedic river goddess (the actual river Sarasvati has now disappeared but she may also be linked to the Indus, etc.).
In her Vedic capacity her waves are said to smash mountains and her voice is the roar of the torrent. Since her source of strength is the primal water, she is inexhaustible and she is the bringer of fertility and bountiful harvests.
Thus, by inference, she also provides prosperity. Her presence purifies and, in antiquity, she slew Vrtra, the demon god of chaos. She was invoked on the sacrificial field as a Vedic goddess.
In later Puranic literature Sarasvati (Brahmi) becomes the consort of the creator god Brahma. Other texts place her in contention with Laksmi, the consort of Vishnu. She is also syncretized with the goddess Vac.
She is said too have invented Sanskrit and is identified as the goddess of wisdom and art. Her festival is held in late January or early February. Being the patroness of students, pupils offer her their books and supplies before they begin classes. Her image often appears on portals of school gates.
Generally, she is depicted with four or two arms. Her color is white. She may ride on a swan, peacock, or lotus.
The lute, in particular, is included among her attributes as well as the arrow, bell, book, bow, conch, club, hook, prayer wheel, rosary, water jar, and other items.
She infrequently appears three headed, and may offer a piece of sugar cane or a flower to Brahma. A.G.H.
Jordan, Michael, Encyclopedia of Gods, New York, Facts On File, Inc. 1993, pp. 228-229