Saraswati, also known as Veenavadini (Goddess who plays Veena, the musical instrument) is the Hindu goddess of knowledge, music, art, speech, wisdom, and learning. She is a part of the tridevi of Saraswati, Lakshmi, and Parvati. She is generally shown to have four arms, holding a book, a rosary, a water pot and a musical instrument called Veena. Each of these items have symbolic meaning in Hinduism. She is usually depicted near a flowing river or another body of water, which depiction may constitute a reference to her early history as a river goddess.

The most famous feature on Saraswati is a musical instrument called a veena, represents all creative arts and sciences,[28] and her holding it symbolizes expressing knowledge that creates harmony.[4][30] Saraswati is also associated with anurāga, the love for and rhythm of music, which represents all emotions and feelings expressed in speech or music. Scholars hold that as Saraswati is the goddess of learning, the most evolved string instrument in a given age was placed in her hands by contemporary artistes. 

The veena has a recorded history that dates back to the approximately 1700 BCE. Eminent veena player E. Gayathri has mentioned in many interviews that the Aitareya Upanishad contains a verse stating that human beings are the veena created by God (daiva veena) and the wooden Saraswati veena is the man-made veena (maanushi veena). According to her, the veena is resemblant of the human skeleton, where the resonating kudam represents the skull, the dandi and the lion (Yali) face the human backbone, and the twenty-four frets on the fretboard representing the 24 vertebrae of the human spine. 

Saraswati is generally shown to have four arms, but sometimes just two. When shown with four hands, those hands symbolically mirror her husband Brahma's four heads, representing manas (mind, sense), buddhi (intellect, reasoning), citta (imagination, creativity), and ahamkāra (self consciousness, ego). Brahma represents the abstract, while she represents action and reality.

-Wikipedia