Very little.
Bishop Asser, a contemporary of Alfred's who wrote a biography about him mentioned her, But only briefly.
From him we learn that:
She was named Osburh
She was the daughter of Olsac, who was a courtier to Aethelwulf and who had family links to the chiefs of the Isle of Wight, which would most likely make him of Jute extraction.
She is described as religiously devout.
She had at least 6 children, oh whom Alfred was the youngest son.
She gave birth to Alfred circa. 849. Asser writes that this happened on the border between Wessex and Mercia, but that could just be political propaganda to establish Alfred's claim to both kingdoms.
She encouraged Alfred's love of reading and learning.
Although she only plays a small part in the biography, I think the fact that she is linked explicitly with Alfred's early education shows that she likely did have a significant role in influencing the kind of King he would become.
http://www.medievalists.net/2014/10/02/osburh-mother-king-alfred-great/