Hindu Deities

Saraswati, also called Vak Devi, is the godess of creative arts, knowledge and speech. She is Brahma's "divine consort", and Brahma is believed to have endowed her with all of his own creative thought. Her name 'Saraswati' derives from the Sanskrit words 'sara' for essence, and 'swa' for self.
The palmleaf scroll and mala she is holding and her white dress stand for knowledge. The white lotus Saraswati sits in also is a symbol of true knowledge, and her position indicates that she herself is rooted in true knowledge. Saraswati's veena indicates her power in creative arts, but also the person's duty to "tune his mind and intellect in order to find true harmony with the world."
The left side of her body is meant to symbolize aspects of the heart, and her right side, actions of the mind. The pile of books to the left tell onlookers that to find balance, and use their knowledge with temperence of emotion. The swan is said to be able to tell good milk from a mixture of milk and water with its beak. Having a swan often as her carrier and usually in pictures of her indicates the value of learning right from wrong, and using that knowledge to serve others. The peacock waiting to carry Saraswati supports the values symbolized by the swan, but also promotes determination in the quest for true knowledge. A peacock is known to be unpredictable and fickle, two traits not valued in Hinduism.
Saraswati is also usually shown with four arms instead of two. The front two arms stand for Saraswati's presence on Earth, and the back two stand for her presence in the spiritual world. The four hands each represent a different aspect of the human character; the mind, intellect, consciousness and ego. The placement of each objects Saraswati holds can display different messages depending on which hand she holds them in. For instance, if the mala is in her back right hand, that image symbolizes the mergeance of true knowledge earned with love and devotion with the ego, which amounts to moksha.
Mantras performed to Saraswati are believed to help in studying and concentration; Saraswati is often admired by teachers and students.

Sources
http://www.sanatansociety.org/hindu_gods_and_goddesses/saraswati.htm
All quotes from: http://www.vedic-arts.com/golden-pic/picure-thumb/saraswati.jpg
Image: http://www.vedic-arts.com