Worship of Saraswati Devi dates back to the early Vedic period in India (1500 BCE), where she was the presiding spirit of a sacred and possibly mythical river. The name of the river is believed to be derived from the proto-Indo-Iranian *sáras-vat-ī, which supposedly means “marshy” or “full of pools”. Another proposed etymology derives her name from the root *sar, which means “flow”. Though this latter theory has been widely repeated, it was apparently not favored by Manfred Mayrhofer, a linguist specializing in Sanskrit and Indo-Iranian languages.(1)
In modern worship, Saraswati’s origins as a river deity have been obscured. She is a deity of wisdom, and a patroness of learning and the arts. Modern commenters sometimes derive her name from Sanskrit Sāra and Sva, meaning of “essence of self-knowledge”. While not a historically valid etymology, it certainly captures Lady Saraswati’s character.
(1) Information taken from Wikipedia entry “Sarasvati River“