The above line comes from Kate Keller, Helen Keller's mother. She says it when Annie Sullivan arrives at the Keller residence to teach Helen the groundbreaking methods of sign language she learned at the Perkins Institute.

Judging by the quotation it's clear that Kate is somewhat surprised by Annie's age and youthful appearance. She had been expecting a "desiccated spinster," meaning that she assumed Annie would be an old, unmarried woman without much vitality. In those days, teachers were generally expected to be quite mature and to have years of experience behind them. So, when Kate sees Annie for the first time, she's somewhat taken aback that someone this young should be offering her services as a teacher.

But as well as the education she received at the Perkins Institute, Annie has an advantage over the competition in that she herself is partially blind and therefore has a unique insight into what is the most appropriate teaching method. Kate may not be able to understand this yet; she still equates expertise with age. But in due course, she'll discover that Annie's education, combined with her own experience of disability—not to mention personal qualities such as kindness and patience—make her the best teacher that Helen could possibly have.