Saraswathi is the goddess of gnana (knowledge and wisdom). She holds gnana mudra. This nama describes the goddess that gives gnana. She removes the masks of ignorance formed due to dwaita and teaches adwaita. This leads to moksha (liberation).
It is said like this in Matsya purana. Brahma did tapasya with an intention to begin the creation. Then 10 male children and 10 female children emerged from his body. The last one of them is Shata roopa. She is also called Saraswathi.
It is said like this in Brahma Vaivartha purana. Saraswathi came from the tongue of divine mother Radha.
It is said like this in Rigveda. There was a great war between Indra and Shambarasura. Indra prays Saraswathi to reveal the secrets of Shambarasura's fort. while finding them, Saraswathi gets entrapped in the fort and loses some of her original glory. That is why pure Sanskrit has become Prakritic.
'Ime' (pronounced like 'ime' in chime) is vagbeeja. Those who meditate upon this will acquire knowledge of all sciences.
A story from Devi Bhagavatam - Once upon a time, there used to be a brahmin called Devadatta. He had no children. With an intention to have children, he started putrakameshti yaga on the banks of river Tamasa. suhrota of that yaga is Brahma. Yagnyavalka is adhvarya. Bruhaspathi is hotha and Gobila is udghatha. As the yaga started, Gobila started chanting Sama veda. While chanting, Gobila took an abrupt pause due to breathlessness. That resulted is improper Swara(pitch). Devadatta chided Gobila for that mistake. Gobila could not bear the insult. He said, "chanting vedas at high pitch is not a child's play. It requires lot of effort and concentration. Due to old age, I was unable to hold breath long enough. You shouldn't have spoken to me that way. You disregarded all my good efforts. I am hurt. I am cursing you that you will surely beget a son due to this yaga, but he will be a fool". After sometime, devadatta's wife gave birth to a male child. His name is Utadya. He grew up. But could not learn anything. He failed in all shastras and became unfit for a brahmin. Other brahmins in the society made a mockery of him. Unable to bear it, Utadya ran to the forest and started meditation. One day in the forest, a hunter was chasing a wild boar. It ran away from the hunter and came towards Utadyas ashram. Seeing it Utadya said 'Ime' to shoo it away. Intuitively he started meditation upon 'Ime' from then onwards and became a scholar in many sciences.
It is said like this in Sharada tilakam - You can offer oblations to goddess Saraswathi with the following flowers. Jaji, Malli, Pogada, Tamara, Mandara, Mogali, black Lotus etc. You can use flowers that blossom as per season. However, you should not use flowers that are worn, stolen, broken, lying with hair/dirt and bitten by insects. You should not pluck flowers after noon.
You will become a genius if you perform havan with red Lotus, Palasha, Bilwa pushpa mixed with honey.
She is goddess of knowledge. All those sacred books that describe Brahma also talk about her. Rig veda has saraswathi suktam. It also has 10 shloka maha mantras of Saraswathi.
Veenaadhaare! Vipula managala daana sheele!
Bhakaartinaashini virinchi hareesha vandhye!
Keerthi pradem khila manorathe! Mahaare!
Vidyaapradaayini! Saraswathi! Noumi Nityam ||